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NOTES AND QUESTIONS 

FOR THE 

DYNAMO LABORATORY 


l/ BY 

F. C. CALDWELL 
''and 

F. A. FISH 


PUBLISHED AT 


COLUMBUS, O 




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PRINTED AND FOR SALE BY 
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TABLE OF CONTENTS OF PART I. 
CHAPTER I. 

NOTES. page 

Objects of work in dynamo laboratory. 9 

Order of operation . 9 

Grades. 10 

Tools . 11 

Laboratory reports ... . 11 

Curves. 12 

Measuring instruments.... 13 

Calibration . 13 

CHAPTER II. 

QUESTIONS ON DIRECT CURRENT LABORATORY 
EXPERIMENTS. 

1. Calibration. 15 

2. Resistance, study of. 16 

3. Windings and constants of dynamos. 16 

4. Connections of dynamos. 17 

5. Series and parallel resistance. 17 

6. Study of instruments. 18 

7. Fuse-wire tests. 19 

8. Location and determination of faults. 19 

9. Preliminary to the running of machines. 20 

10. Speed-potential curve. 21 

11. Magnetization and hysteresis. 22 

12. Series characteristic. 22 

13. Shunt characteristic.. 23 

14. Compound characteristic and regulation. 24 

15. Potential around the commutator. 24 

16. Parallel running of compound machines. 25 

17. Magnetic leakage. 26 

18. Shunt motors. 26 

19. Series motors and controllers. 28 

20. Losses and efficiency of combined motor and generator- 28 

21. Arc generator regulation. 28 


3 






































































PREFACE. 


The use of these “Notes and Questions” involves to 
a greater or less degree a system of laboratory instruction. 
While it may be claimed that the ideal method is that of 
the rediscovery by the student of the laws studied, it must 
be admitted that this is generally impracticable in engineer¬ 
ing laboratories. Time for such a thorough system is usually 
wanting, and further, many who will make useful engineers 
have not, and never will have the talent of the discoverer. 
With such the method of rediscovery leads either to so 
much time being consumed with each piece of work, that 
too little ground is covered; or more usually, the stu¬ 
dent will get enough idea to go through with the experi¬ 
ment, and will then pass on to the next having no proper 
understanding of what he has done. On the other hand, 
if dependence is placed entirely upon a textbook giving full 
directions for carrying out the work, the less careful student 
will be satisfied when he has followed the instructions, 
regardless of how much or how little he has got out of them. 

In view of these facts the accompanying scheme was 
devised for the purpose of obliging the student to thor¬ 
oughly understand what he is doing. The method and 
most of the matter has been in use several years, and has 
worked so well that the authors venture to hope that in its 
published form it may prove useful to others. 

7 






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V 




CHAPTER I. 


NOTES. 

OBJECTS OF WORK IN DYNAMO LABORATORY. 

IN ORDER OF IMPORTANCE. 

ist. Facility in handling problems connected with 
dynamo machinery and engineering. 

2nd. Judgment, accuracy, skill and quickness in per¬ 
forming laboratory operations. 

3rd. Knowledge of particular facts and methods met 
with in the work. 

ORDER OF OPERATION. 

ist. Study thoroughly the work to be done; that is, 
be sure before beginning that what is sought and how it is 
to be obtained, is well understood. This will generally be 
accomplished by careful use of the questions and references. 

2nd. Make, in note book, neat diagrams of all con¬ 
nections of machine and instruments used. 

3rd. Make careful calibration of all instruments, but 
only through the range where readings are to be taken. 
If more convenient, this may be done at some other time 
during the test. 

4th. Following the diagrams, set up and connect all 
apparatus to be used with as much speed as possible. The 
more active the part taken the more profit will be received 
from the work. 

5th. Look over all connections again to be sure they 
are right, then try cautiously with the current. 

6th. Go over the whole course of the experiment as a pre¬ 
liminary run , taking only such readings as are necessary to 





10 


NOTES AND QUESTIONS 


show that everything is right. If anything is wrong, repeat 
the preliminary run till all is as it should be. 

7th. Make the final runs, taking enough readings to 
get a good curve—generally about ten. The man whose 
instrument is most hard to read, or who is keeping a con¬ 
stant, should call, “Ready—Now,” and then give the num¬ 
ber of the observation, all the other men entering their 
readings opposite the same number. If readings are un¬ 
steady, either take the average of three or five or let “Now” 
be called till every observer is sure of a good average read¬ 
ing. Always, if possible, take two runs. 

8th. Immediately, if practicable, let each man read his 
figures for the others to note. 

9th. Work up in company the results obtained, each 
man doing his share, and plot the curves. If not satis¬ 
factory, repeat. 

In general where two or more are working together 
they should take turns in being responsible for the cool and 
proper running of the machinery used, including bearings, 
belts, commutators and windings. Anything, excepting 
sometimes a commutator, which is too hot to hold the hand 
on, is in a dangerous condition, and damages resulting, 
unless someone is ready to assume the blame, will be 
charged to all. Every man is personally responsible for 
returning to its place, in good condition every piece of 
apparatus and tool which he takes out, and if anything is 
out of order before or after use, it should be reported im¬ 
mediately. 

GRADES. 

Note book, curves and report blank must be handed in on 
the day set, and except in case of acceptable excuse, grade 
is discounted if reports are over due. Before the end of the 
term one blue print of each curve accepted must be handed 
in, to be filed for record. The grades depend upon com¬ 
pleteness, accuracy and neatness in note book and curves, 
ability, quickness, carefulness, industry and freedom from 
“accidents” in the laboratory. 


DYNAMO LABORATORY 


11 


TOOLS. 

Each student must provide himself with a small screw¬ 
driver and pair of pliers. A small wrench and a compass 
are also desirable. All tools should be marked with the 
owner’s name, which may be done by etching with dilute 
nitric acid, using melted compound for protecting the 
metal, and writing while the latter is soft. It is also best 
for each student to be provided with about four thumb¬ 
screw connectors. 

All easily portable instruments must be replaced at 
the end of each day’s work, and all other instruments, 
apparatus and machines disconnected and connecting cable 
and wires put away unless allowed to remain by special 
permission. 


LABORATORY REPORTS. 

To develop habits which will conform with the methods 
of practical work all notes, readings and results in connec¬ 
tion with the laboratory work should be recorded as they 
are obtained and for permanent reference in a convenient 
and well made note book.f 

This laboratory note book should have owner’s name 
printed on slips of paper on the front cover, upper right 
hand corner and on the back, and the pages should be 
numbered. The books should be kept as clean and neat 
as possible, while always being used in the laboratory. 
Never make any notes whatever on pieces of paper or 
other note books. Do not crowd matter. Leave one or 
two sheets at the beginning and after each test. The 
readings should be entered directly, leaving necessary inter¬ 
mediate columns for corrected values and results. Put 
title on right hand page, and use several pages for descrip¬ 
tion, answers to questions, sketches of connections, and all 
data of machine, test, etc., that may possibly be useful, 
including name, capacity, potential, speed, etc., of the 

*These may well be supplied by the laboratory; see appendix. 

♦See Appendix. 



12 


NOTES AND QUESTIONS 


machine, men working, and positions occupied by them, 
names and numbers of instruments, constants used, etc. 
Use conventional symbols as found on page 13 of Part II. 
In all diagrams, wiring should be represented by lines par¬ 
allel with the edges of the page. At top of each page 
put name of test, date and reference to curves, etc. All 
columns should be carefully headed. These headings 
should include in each case the number of the instrument 
used. Make figures small and with pen or with pencil, 
neither too hard nor too soft. Always correct readings for 
errors of instruments. Refer to curves by number. 

CURVES. 

These may be either to show some property or pecu¬ 
liarity of the machine tested, or they may be for the pur¬ 
pose of comparing two instruments, as a calibrating curve 
of a voltmeter. 

If for the former purpose the exact value of the scales 
chosen is of secondary importance, but the curves should 
be so drawn as to show to the best advantage the property 
which it is intended to bring out. They should usually 
incline in general direction about 45 degrees with the axes, 
and should not be too large; there is no advantage in taking 
more than one division of the paper to represent one divis¬ 
ion on the instrument read. The abscissae should be the 
independent variable, the ordinates the dependent. The 
broad margin should be at the left or the top. 

If for calibration use, the scale should also be chosen 
for convenient reading, i. e., 1 division equal 1-5, 1-4, 1-2, 1, 
2, 4, or 5. Always give the scale, either on the margin 
or along the curve, and in whole numbers, not in observed 
values. Points should always be shown by circles, 
crosses, etc.: circles are best and should be made with a 
bow pen. In general as many curves as convenient deal¬ 
ing with one machine or set of tests should be placed 
together on one sheet. If they cross each other too much 
for dearness different linings or different colored inks 


DYNAMO LABORATORY 


13 


may be used. Always name each curve, or indicate it by 
letter or number reference. If several curves have one 
scale in common, put that on the margin, and the other 
scales along the curves, or in columns along the other 
margin. Put on each sheet all suitable data, including 
constants, name of student, date and reference to page of 
note book. Sometimes it is best to show a curve to two 
different scales to bring out different parts. 

On printed report blanks, make out and hand in one 
report of each successful experiment, giving besides full 
data called for on blank, all readings taken and final results, 
i. e., those from which curve is plotted. 

MEASURING INSTRUMENTS. 

Always handle with the greatest care. Avoid jar¬ 
ring, as by setting down hard, dropping, moving a table 
with instruments on it, etc. Never use a magnetic instru¬ 
ment within five feet of a machine, or within one foot of 
other instruments or masses of iron. Never break a current 
at the terminals of an ammeter. In changing the terminals 
of a voltmeter, always change at the machine or circuit 
end. 

In wiring up instruments, always put zvires through 
holes in table provided for that purpose; or otherwise secure 
them so that it will be impossible to pull the instruments 
on to the floor. Avoid as much as possible crossing wires. 

Remember: An ammeter has very low resistance. 
A voltmeter has very high resistance. With low reading 
ammeters and possibility of higher currents alzvays use fuse. 
It is better to place a low reading ammeter where it can be 
short circuited, and then only open the circuit when ready 
to read. 

CALIBRATION. 

No instrument is ever absolutely correct except orig¬ 
inal standards, as standard meter in Paris, etc., and no 
quantitative results have commercial or scientific value, 
unless it is possible to trace back the standardization of the 


14 


NOTES AND QUESTIONS 


instruments used to their original standards and to be sure 
of the comparison within a given per cent, of error. No 
ordinary electrical instruments, especially portables in com¬ 
mon use, can be relied upon to keep their constants for 
any length of time. They should be compared with stand¬ 
ard instruments at least once for every test; and, in case of 
importance, both before and after the test. To make com¬ 
parison with other calibrations possible, readings should 
be taken for multiples of ten on the calibrated instrument, 
and properly recorded on blanks supplied for that purpose. 

The profit that can be got from the laboratory work 
depends very largely upon the activity of the student him¬ 
self. Every moment should be employed. If the condi¬ 
tions are such that nothing can be done on the experiment 
in hand progress may be made by working ahead on the 
questions for the next experiment. There is much more 
work that could be done than there is time for in the course; 
the most interesting is at the end, and how much of this the 
student gets depends largely upon himself. 


CHAPTER II. 


QUESTIONS ON DIRECT CURRENT LABORATORY 
EXPERIMENTS. 

Before performing any experiment which has been assigned, 
study carefully the questions and references. Where references 
are not given, look up the subject in the text-books which are 
available. In some cases answers to part of the questions may 
better be deferred till after the experiment. Write the answers 
to the questions neatly in the note books without crowding, and 
leaving a line blank after each answer. For the earlier experi¬ 
ments very detailed questions are given, but later on the ques¬ 
tions become more general, leaving to the student the exact form 
of the discussion, which however should be no less full. 

1 

CALIBRATION. 

(a) Sketch connections for comparing with the 
standard, an ammeter having the same range. Also one 
having a different range. 

(b) Same for a voltmeter. 

(c) Given a 20 KW. no volt generator, with but 
three horse power available for running it, how can a 125 
ampere ammeter be calibrated? 

(d) Given a potential equal to the highest to be cal¬ 
ibrated and a high resistance, all points of which are acces¬ 
sible, make a diagram of connections for calibrating a volt¬ 
meter from zero to its capacity. 

(e) Make a diagram of all connections in the calibrat¬ 


ing room. 


15 




16 


NOTES AND QUESTIONS 


2 

STUDY OF RESISTANCE. 

Examine resistances assigned, diagram each of them 
and determine the following: 

(a) Resistance of its segments. 

(b) Highest possible resistance. 

(c) Lowest possible resistance. 

(d) Carrying capacity (determined for metal, as point 
where paper is charred; for lamps by their proper voltage). 

(e) Largest power that can be absorbed. 

(f) Combinations of switches to proceed stepwise 
from highest to lowest resistance. 

(g) Effect of varying current on value of resistance. 

N. L. M., Vol. I, 208 . 

3 

WINDINGS AND CONSTANTS OF DYNAMOS. 

(a) In general, the resistance of what three windings 
of a dynamo are to be measured? 

(b) Which may be absent, and in what sorts of ma¬ 
chines ? 

(c) Which of these windings are generally made up 
of two or more equal parts joined in series? Which is 
made up of two or more equal parts in parallel? 

(d) What two methods of resistance measurement are 
most adaptable to this, and in general to dynamo work? 

(e) Diagram and explain how, by each of these 
methods to obtain the resistance of each of the parts which 
are in series without disconnecting them. 

(f) Can the individual resistance of each of the par¬ 
allel parts be obtained without disconnecting them, and 
why? 

(g) What inconstant element makes the exact deter¬ 
mination of the armature resistance difficult? Suggest a 
method for reducing this error. (Always follow this 
method, taking at least five readings.) 


DYNAMO LABORATORY 


17 


(h) Suggest a method for measuring the contact 
resistance of the brushes. What precaution to be taken in 
regard to contacts? 

(i) How may the length of the wire on the field 
magnet be determined? How the approximate number of 
turns ? 

(j) Under what circumstances will the resistances 
measured not be the normal running resistances of the 
machine ? 

(k) In such cases how obtain from them the true 
running resistances? 

(n) When impossible to apply micrometer or wire 
guage how may the size of wires be obtained? 

Machines often run from 75° to ioo° Fahrenheit above 
the temperature of the atmosphere. One hundred and 
eighty degrees is a fair value. Determine running resist¬ 
ance of a series and of a shunt machine; number of turns 
and size and length of wire on fields and armature; brush 
contact resistance, noting also kind of brush used, circular 
mils per ampere in field and in armature. 

T. D. E. M., Ch. Ill; S. & B., 328 to 345; ; H. & K., Ch. II; N. L. 

M. , Vol. II., 8. 

4 

CONNECTIONS OF DYNAMOS. 

(a) Study the machines assigned, to determine whether 
alternating or direct; series, shunt or compound. Make 
diagrams of connections of each machine and its regulator. 
Give data as to voltage, current and output, also types of 
armature and field magnets. 

T. D. E. M., Ch. Ill and VIII; S. & B., 328 to 345; H. & K., Ch. II.; 

N. L. M., Vol. II, 8. 

5 

SERIES AND PARALLEL RESISTANCES. 

(a) Give complete directions for calculation of resist¬ 
ances in series and parallel. Make several entirely differ- 



18 


NOTES AND QUESTIONS 


ent combinations of the segments of the assigned resist¬ 
ances, measure the resistance of each segment separately, 
calculate the resistance to be expected in each combina¬ 
tion and verify the result by experiment. 

s. & B., 22 to 30 . 

6 

STUDY OF INSTRUMENTS. 

(a) Name three essentially different types of magnetic 
measuring instruments and give examples. 

(b) Which of the above types cannot be used for 
measuring alternating currents and why? 

(c) Explain the principles employed in the construc¬ 
tion of alternating current instruments. 

(d) Describe in detail and with diagrams the con¬ 
struction and operation of the instruments assigned. 

(e) What three reasons why in stationary magnet 
types the air-gap should be made as short as possible? 

(f) Why is uniformity of field desirable? 

(g) What points are gained by having two springs 
instead of one, for bringing the needle to zero? 

(h) Give a structural detail by which error due to 
parallax is avoided. 

(i) Explain, with diagram, the essential differences in 
the circuits of voltmeters and ammeters, giving parts pecu¬ 
liar to each. 

(j) Give method for using a voltmeter for pressures 
above its range. Same for an ammeter. 

(k) What difficulty that does not exist in the above 
method for voltmeters is found in the case of ammeters, 
and why? 

( l ) Explain measurement of current by means of 
milli-voltmeter and shunt. 

(m) Discuss the effect of temperature on voltmeters 
and on ammeters. 


DYNAMO LABORATORY 


19 


(n) How could the heating of a wire be used to 
measure current? (Note.—This forms an important though 
not very accurate class of instruments.) 

(o) Describe a method for using electrostatic attrac¬ 
tion for an instrument. 

(p) Give advantages and disadvantages of this type of 
instruments. 

(q) Give method of making these instruments for low 
voltages, and for damping the needle. 

(r) What type of instrument makes use of electro¬ 
magnetic repulsion of parallel coils? Describe. 

S. & B., parts of Chs. IV & VI; El. W., Vol. XIX, 217, 233, 277; 
catalogues. 

7 

FUSE WIRE TEST. 

(a) How should the fusing current for fuse wire vary 
with: (i). Length between terminals? (2). Time of 
flow of current? (3). Size of terminals? 

Take two sizes of wire and leaving current on for ten 
seconds find fusing current for 1-4", 1", 2" and 3". Try 
three pieces of each length and take mean of results. 

With two sizes of wire try several currents in the 
vicinity of the fusing current, and note time required to 
fuse in each case; get a mean of three results for each cur¬ 
rent. 

Find current to fuse two different sizes of wire in ten 
seconds on different sized terminals. 

Short-circuit fuse in each case until the current is ad¬ 
justed. Plot the results. 

Trans. A. I. E. E. 93, Vol. X, 251. N. L. M., Vol, II, 74. 

8 

LOCATION AND DETERMINATION OF FAULTS. 

BY RESISTANCE METHODS. 

(a) Name the different kinds of faults that may occur 
in the winding of a dynamo. 


20 


NOTES AND QUESTIONS 


(b) What is meant by a “ground”? 

(c) If there is no ground, how closely can an open 
circuit in the field winding be located by resistance meas¬ 
urement ? 

(d) Same if there is a complete ground at the open 
circuit ? 

(e) Give a method, based on the principle of Wheat¬ 
stone’s bridge for the location of a ground. 

(f) Give a method for determination by resistance 
method of the proportion of a coil that is short-circuited. 

(g) In the case of a formed coil, give a method for 
determining in what part of the coil a short circuit is located. 

(h) If the whole, or a large part of a coil were short- 
circuited, suggest a method for determining that fact with 
current, but without the use of instruments. 

(i) Given a voltmeter of known high resistance, de¬ 
scribe a method, by using it also as a current meter for 
determining the resistance of a partial ground. 

(j) How determine the highest resistance that can be 
measured with a given instrument and a given voltage? 

(k) Give directions for locating, by resistance meas¬ 
urement, an open circuit in a closed coil armature. 

1 ( 1 ) Same for a ground. 

(m) Same for a short-circuited coil. 

(n) Same for abnormal resistance between holder and 
brush and between brush and commutator. 

9 

PRELIMINARY TO THE RUNNING OF 
MACHINES. 

Give in detail the effects on the action of the machine 
of the following, together with the reasons therefor: 

(a) Not having the brushes set at the correct angle. 

(b) Not having the brushes opposite. 

(c) Letting the brushes spark. 


DYNAMO LABORATORY 


21 


(d) Letting the commutator become covered with 
film of oil and dirt. 

(e) Letting the bearings get dry. 

(f) Suddenly breaking the field circuit. 

(g) Putting too much current through the armature. 

(h) Putting resistance in the main circuit of a motor. 

(i) In the armature circuit. 

(j) In the field circuit. 

(k) Effect on speed,—of shifting the brushes. 

( l ) Increasing the number of ampere turns on the 

field. 

(m) Effect of reversing the direction of the current 
through the whole machine. 

(n) Through the armature. 

(o) Starting motor without starting resistance box. 

(p) Putting current into the armature with field 
circuit open. 

10 

SPEED POTENTIAL CURVE. 

n C 0 

(a) Given the E. M. F. of a generator ==-^- 

how should it vary with the speed, i. e., what should the 
curve be if the flux is constant. 

(b) What must be done to keep the flux constant? 
fc) Will it do to self excite the machine during the 

test, and why? 

(d) Suppose the field current to be increased or 
decreased, and then brought directly to its former value, 
what will be the effect on the curve, and why? 

(e) How remedy the above effect ? 

Obtain this curve for the machine assigned. 

To get variable speed, use resistance in series with 
motor armature. 

H. & K., 3; T. D. E. M., 45.. 



22 


NOTES AND QUESTIONS 


11 

MAGNETIZATION AND HYSTERESIS. 

(a) What is a magnetization curve? 

(b) What is the difference between a magnetization 
curve and a hysteresis curve? 

(c) Sketch magnetization curves for a dynamo and 
for the iron part of its magnetic circuit, and explain the 
difference. 

(d) What does the general inclination of the curve 
to the X axis indicate? 

(e) What the curvature ? 

(f) How, as to scale, must curves of different ma¬ 
chines be plotted, to be comparable? 

(g) What does the hysteresis curve show? Explain 
with sketch. 

(h) Suppose too great an increase is made in the 
current, and that then it is reduced directly to the required 
value, what effect is produced on the curve? 

(i) How reach the required value without this effect ? 

(j) Why should the speed be kept constant? 

(k) If the speed is not kept as above, how can the 
readings be corrected for it? 

( l ) Can the machine be self-exciting during the test, 
and why? 

(m) Give the process for obtaining a complete hys¬ 
teresis curve, and discuss it as indicating the characteristic 
qualities of the machine. 

Note — Regulate motor speed with resistance in its field. 

T. D. E. M., 122 to 142; Jackson, Vol. I, 195 to 200; N. L. M., Vol. 
II, 15. 

12 

SERIES CHARACTERISTIC. 

(a) Define series characteristic. 

(b) What two different forms of the series character¬ 
istic ? 

(c) Which is observed ? 


DYNAMO LABORATORY 


23 


(d) How is the other obtained? 

(e) What data of the machine must be known? 

(f) Draw an example of a series characteristic and 
explain the effects of speed, internal resistance, air gap and 
quality of iron. 

(g) What element should be kept constant and how 
can it be corrected for if varied? 

Carry test to about 25% overload. Take points closer 
together where the curvature is greater. Take minute 
speed readings and mean electrical readings for that period. 


N. L. M., Vol. II, 14; T. D. E. M., Ch. X; Jackson, Vol. I, 200 to 208; 
S. & B., 345 to 353; H. & K., 209 to 211. 


13 

SHUNT CHARACTERISTIC. 

(a) What two forms of shunt characteristic ? Sketch. 

(b) Which is observed? 

(c) What are “resistance lines,” and how drawn for 
armature and fields? Sketch. 

(d) Describe process for obtaining the calculated 
characteristic. 

(e) What constants of the dynamo must be known 
for the above calculation? 

(f) What is shown by the slope of the upper part of 
the curve, in the external characteristic ? In the total char¬ 
acteristic? (See Jackson.) 

(g) In the external characteristic, explain why the 
upper part drops more rapidly as it proceeds further. 

(h) What is the electrical condition of things in the 
machine when the curve begins to return toward the Y 
axis ? 

(i) What causes the shape of the lowest part of the 
curve ? 

(j) Is it possible to correct for variation in speed and 
why? 

(k) What effect is produced by putting additional 
resistance in shunt field circuit and why? 


24 


NOTES AND QUESTIONS 


( l ) What will be the nature and signification of a 
curve of field current plotted with armature current, the 
terminal E. M. F. being left constant. (This curve is some¬ 
times called the armature characteristic). 

(m) What will be the effect if a shunt machine is sud¬ 
denly short-circuited? Is gradually short-circulated? 

Obtain total characteristic and armature characteristic. 

N. L. M., Vol. II, 17 to 25; Jackson, Vol. I, 200-208; T. D. E. M., 
Ch. X; S. & B.,. 353 to 356. 

14 

COMPOUND CHARACTERISTIC AND REGULA¬ 
TION. 

(a) Sketch connections of a compound machine. 

(b) Explain the difference between long and short 
shunts with diagrams. 

(c) What would be an ideal compound character¬ 
istic? 

(d) Explain the action of the shunt and series coils 
in producing the compound characteristic. 

(e) How will the actual compound characteristic 
differ from the ideal and why? 

(0 What is indicated by a falling characteristic? 
What by a rising characteristic? 

(g) What must be done to remedy the former ? What 
two remedies for the latter? 

(h) Under what circumstance would a rising char¬ 
acteristic be required? 

Take series characteristic and compound characteristic; 
also regulate compound winding for constant potential, and 
for 2% over-compounding. 

N. L. M., Vol. II, 25; H. & K., 208; S. & B., 357-362 

15 

POTENTIAL AROUND THE COMMUTATOR. 

(a) How does the potential vary between consecutive 
segments around the commutator? 


DYNAMO LABORATORY 


25 


(b) What is the cause of this variation? 

(c) What would be the form of the curve if the ma¬ 
chine had but one narrow coil and why? What if there 
were no iron in the armature? 

(d) Discuss the difference between the curve for no 
load, and that for full load, with causes. 

(e) Describe two methods of obtaining curves of 
potential around the commutator. 

(f) Which is the more accurate and why? 

(g) How would reversal of the field under a pole-tip 
be indicated in the curve? 

Take curves with both one and two brushes, sep¬ 
arately excite the field, and take no load and full load 
curves with both strong and weak fields, using two brush 
method. 

N. L. M., Vol. II, 63; T. D. E. M., 63-65; Jackson, Vol. I, 20S; Am. 
Elec., March, 1898. 

16 . 

PARALLEL RUNNING OF COMPOUND 
MACHINES. 

(a) Explain why compound machines will not run 
properly in parallel if only the terminals are connected to¬ 
gether. 

(b) Describe with diagram an equalizer and its action. 

(c) What effect on this action would resistance in 
the equalizer circuit have? 

(d) Discuss effect of form of characteristic on parallel 
running, and method of making characteristics similar. 

(e) What effect on the division of the load will the 
resistance of the series fields have? 

(f) Describe and explain the operation of throwing 
compound machines in parallel. 

Connect up two compound machines with equalizer; 
and, if possible, adjust to take equal or proportional load 
from no load to full load. Vary the resistance of one 
series field and repeat. 

T. D. E. M., 766; Jackson, Vol. I, 230-243; P. & S., 331-340; C. & W., 
49 to 57. 



26 


NOTES AND QUESTIONS 


17 . 

MAGNETIC LEAKAGE. 

(a) Describe fully the various useful and waste mag¬ 
netic paths in a dynamo. 

(b) Explain “coefficient of leakage”. 

(c) Explain briefly methods of calculation of the co¬ 
efficient of leakage. 

(d) Describe methods of determination of the above, 
and also of the leakage in various parts. 

(e) What precautions are necessary in the disposition 
of the wires in the test coil circuits? 

By the above methods obtain both total coefficient and 
also the leakage in various parts of stray field. 

N. L. M., Vol. II, 67; T. D. E. M., 163. 

18 . 

SHUNT MOTORS. 

18 A. MOTOR TORQUE AND REGULATION. 

(a) Give and discuss the equation for the relation of 
torque and current. 

(b) Describe the method of obtaining torque. 

(c) Give method for eliminating the error due to me¬ 
chanical friction. 

(d) Using equation for armature current, discuss the 
regulation of motor speed, by varying (1) armature resis¬ 
tance, (2) field resistance. 

(e) Discuss effect of changing number of field turns, 
the voltage remaining constant. 

(0 Give the effect on the regulation of running the 
motor at different points on its magnetization curve. 

183. EFFICIENCY AND LOSSES BY THE ELECTRICAL 
METHOD. 

(a) Give three expressions for the commercial efficiency 
of a dynamo in terms of input and output and losses. 


DYNAMO LABORATORY 


27 


(b) Give a tabular classification of all sources of loss 
in a dynamo machine indicating which are constant, which 
dependent upon the load and which upon the speed. 

(c) What curves must be taken and what corrections 
made? 

(d) Which losses are proportional to the speed and 
which to the square of the speed? 

1 SC. EFFICIENCY BY BRAKE. 

(a) Describe the Prony Brake, and discuss the theory 
of its use, giving the proper length of the arm for con¬ 
venient reduction of the results. 

(b) What error results if the brake arm is not hori¬ 
zontal? 

Keeping the voltage on the motor constant and normal, 
obtain curves of speed with armature current under the 
following conditions,—* 

(a) With a constant known field current and by vary¬ 
ing the load on the brake,— 

1. With no resistance in the armature or field, 

noting in this case also the readings, 

2. With constant known resistance in the arma¬ 

ture. 

3. With constant known resistance in the field, 

(b) By varying the resistance in the armature circuit,— 

4. With no load, noting also voltage on the arma¬ 

ture, 

5. With a constant load. 

(c) By varying the resistance in the field,— 

6. With no load. 

7. With a constant known load. 

Plot these seven curves on a single sheet. 

From the data secured above, calculate and plot curves 
as follows: iron and friction loss with speed; also, with watts 
input, the following; speed, iron and friction loss, field loss, 
armature copper loss, total loss, electrical output, brake out¬ 
put, efficiency by the electrical method and by the brake 
method. 

T. D. E. M., 501 to 505 , 510; P. & S., 36 to 55; JL & K., Chs. XXV & 
XXVI; N. L. M., Vol. II, 37, 40; Bell, 88-91. 


28 


NOTES AND QUESTIONS 


19 . 

SERIES MOTORS AND CONTROLLERS. 

If 18 has not been taken first, answer questions a, b, 
and c of 18 A. 

(a) Using the equation for armature current, discuss 
the effect of variation of resistance and of field strength upon 
the speed. 

(b) Compare and discuss starting torque and speed in 
series and shunt motors. 

(c) Describe and explain fully the controller and its 
action in starting and in regulating the speed of series 
motors. 

Connect up the controller, start and operate with it 
under various loads, to represent working conditions. 

Get the curve of speed with resistance, with no load 
and with load; also of speed with output, and of starting 
torque with current. 

T. D. E. M., 506; P. & S., 36-55, 481 to 487; S. & B., 469, 470 , 478 , 490; 
H. & K., Chs. XXV & XXVI. Bell, 80-88. 

20 . 

LOSSES AND EFFICIENCY OF COMBINED 
MOTOR AND GENERATOR. 

(a) Describe methods of the operation of two ma¬ 
chines at full load by supplying the losses (1) mechanically, 
(2) electrically; this for both shunt and series machines. 

(b) Discuss determination of combined losses and of 
the efficiencies if equal, of the individual machines. 

Operate the machines assigned and obtain losses and 
efficiency. 

Jackson, Vol. I, 254 to 257; T. D. E. M., 758 to 760; N. L. M., Vol. II, 34- 
P. & S., 356 to 359, 433 to 438. 

21 . 

ARC GENERATOR AND REGULATOR. 

(a) Give the general methods in use for constant cur¬ 
rent regulation. 


DYNAMO LABORATORY 


29 


(b) Describe and explain the machines studied, to 
gether with the auxiliary regulating apparatus. 

Adjust the regulator and obtain regulation curve. 

S. & B., Ch. XI; Jackson, Vol. I, 225 to 229; T. D. E. M., Ch. XVIII; 
C. & W., 163 to 202. 

22 . 

STUDY OF ARC LAMPS. 

(a) Give the functions to be performed by the mechan¬ 
ism of arc lamps of different types 

(b) Give a complete classification of arc lamps. 

(c) Discuss differences between open and enclosed 
lamps. 

(d) Also between direct and alternating current lamps. 

(e) Describe with diagrams the mechanism, of the 
lamps studied. 

(f) Discuss electrical efficiency of arc lamps and meth¬ 
ods of obtaining the same. 

(g) Discuss the regulation of arc lamps, conditions 
affecting the same, and method for its determination. 

Determine the current used, and the volts and watts, 
consumed by the mechanism; also the electrical efficiency, 
and regulation curves with the lamp in both good and bad 
adjustment. 

N. L. M., Vol. II, 46; S. & B., 615 to 638. 


23 . 

PHOTOMETRY. 

(a) Give and explain the laws of light as applied in 
photometry, and also the unit used. 

(b) Describe and explain the photometers and auxil¬ 
iary apparatus used. 

(c) Discuss fully the measurements assigned and 
the methods of carying them out. 

(d) What special difficulties in arc photometry and 
what precautions are necessary? 


30 


NOTES AND QUESTIONS 


(e) Discuss the efficiency of incandescent arc lamps. 

(f) Discuss the life of incandescent lamps. 

(g) Discuss fully the results obtained. 

S. & B., 590 to 615; N. L. M., Vol. II, 212 to 223 , 318 to 329, 342 to 

346. 

24 . 

ILLUMINATION. 

(a) Give and explain the laws and units involved in 
a study of illumination. 

(b) Explain conditions, other than strength and po¬ 
sition of the source of light, that affect illumination. 

(c) Describe and explain the apparatus used. 

(d) Discuss fully the measurements assigned and the 
results obtained. 

S. & B., 704, 705. 

25 . 

ACCUMULATORS. 

(a) Discuss the chemical composition of a charged cell, 
and the changes resulting from discharge. 

(b) What are the two principal classes of lead cells? 

(c) Discuss the specific gravity of the electrolyte, and 
its effects on the E. M. F. of the cell. 

(d) Draw curves of charge and of discharge with time, 
and discuss. 

(e) Give the general relation between discharge rate 
and capacity, and between discharge rate and efficiency. 

(f) Give the effects of excessive current, and of over¬ 
charge. 

(g) To what E. M. F. per cell should the discharge 
be carried, and what is the advantage of not discharging 
too far? 

(h) What precautions are to be taken when mixing 
sulphuric acid with water? 

(i) To what E. M. F. should the charge be carried 
and what is the effect of carrying it too far? 

(j) Give directions for determining the efficiency of the 
cell, noting particularly the precautions necessary to insure 


DYNAMO LABORATORY 


31 


that the cell shall be in the same condition at the end of the 
test as at the beginning. 

(k) Give directions for measuring the resistance of the 

cell. 

Obtain curves of E. M. F. and time at a constant rate of 
charge and at two different constant rates of discharge. De¬ 
termine the resistance of the cell, and its efficiency. Obtain 
special curves of E. M. F. and time for short intervals after 
closing and opening the circuit, both for charge and dis¬ 
charge. 

S. & B., Ch. XIV; Trans. A. I. E. E., Vol XI, 302; XII, 585. 

26 . 

STUDY OF LIGHT AND POWER PLANT. 

Describe in detail with sketches and diagrams such 
of the following features as are present in the plant studied. 

(a) The coal carrying machinery; 

(b) The stokers; 

(c) The boilers; 

(d) The ash handling machinery; 

(e) Feed water supply; 

(f) Engines and generators; 

(g) Condensing plant; 

(h) Switch-board, giving directions for making all 
possible combinations of machines and circuits, and func¬ 
tions of all apparatus; 

(i) Power distribution; 

(j) Light distribution; 

(k) Heat distribution; 

( l ) Give all steps to be followed in starting up each of 
the engines and generators; 

(m) In changing load from one machine to another; 

(n) In shutting down; 

(o) In throwing machines in parallel. 

In above descriptions give full data, such as capacity, 
pressure, etc. 



CHAPTER III. 


QUESTIONS ON ALTERNATING CURRENT LABORA= 
TORY EXPERIMENTS. 

27 . 

SIEMENS ELECTRODYNAMOMETER. 

(a) Describe and sketch the instrument. 

(b) Explain its theory, action and use. 

(c) Explain the effect of reversing one of the coils. 

(d) Does the angle of lag of the current in the 
circuit have an effect upon the correctness of the dynamo¬ 
meter reading? 

(e) Give the probable effect of the mercury in contact 
cups not being clean. 

(f) What precaution should be taken to avoid the 
effect of the earth’s field, when calibrating with direct cur¬ 
rent? Why is this effect not present when using with alter¬ 
nating current? 

(g) Why are very low readings not liable to be 
accurate? 

(h) To reduce sensitiveness one-half what change 
should be made in the design ? 

(i) How may the instrument be used to determine 
difference of phase between two currents? 

N. L. M., Vol. II, 69; S. & B., 102 to 107; F. & W., 29 to 31; Jackson, 
Vol. II, 128. 

28 . 

WATTMETERS. 

(a) Explain the theory, action and use of the dynamo¬ 
meter wattmeter. 

(b) Explain the error resulting from appreciable in¬ 
ductance in the shunt circuit. 

32 



DYNAMO LABORATORY 


33 


(c) What is the correcting factor, and why is it not 
practicable to use it? 

(d) Assuming a maximum lag in the line how may 
the maximum allowable inductance in the shunt circuit be 
calculated ? 

(e) What is the error with the shunt coil connected 
outside of the series coil? 

(f) What with it connected between the series coil 
and the load? 

B. T., 369 to 374; S. & B., 542 to 544; Jackson, Vol. II, 131 to 135; 
F. & W., 36 to 38. 


29 

STUDY OF INDUCTIVE CIRCUITS. 

(A) IMPEDANCE DIAGRAM. 

(a) Having given the frequency of an alternating 
current and the resistance of the circuit, explain how to 
obtain the coefficient of self-induction. 

(b) Show how, with these data, to construct the tri¬ 
angle of impressed, active and inductive E. M. Fs. (virtual.) 

(c) How change this to the triangle of maximum E. 

M. Fs? 

(d) How change to the impedance triangle? 

(e) The ratio of what quantities determines the shape 
of this triangle? 

(f) What is this ratio called? 

(g) Given three voltmeters and a known non- 
inductive resistance, how can the above triangles be deter¬ 
mined ? 

(h) Explain how to use but one or two voltmeters 
for this. 

(i) What would be the effect of using a voltmeter 
which took an appreciable amount of current, across the 
outside of the circuits ? 

(j) Also across the non-inductive circuit, and how 
eliminate the effect if the voltmeter is non-inductive? 




34 


NOTES AND QUESTIONS 


(k) What effect if used across the inductive circuit? 

(l) In a circuit without iron, what effect on the coeffi¬ 
cient of self-induction would changing the current have ? 

(m) Having constructed the triangle for the coil 
without iron, what would be the effect on it of inserting an 
iron core? 

Construct the virtual E. M. F. and impedance triangles 
by two methods, both with and without iron. 

(B) VARIATION OF RESISTANCE IN AN INDUCTIVE 

CIRCUIT. 

(a) With a constant impressed E. M. F. and a con¬ 
stant inductance, what will be the locus of the right-angle 
vertex of the E. M. F. triangle ? 

(b) What will be the locus of the current ? 

(c) What will be the value of the current when the 
resistance is zero? 

Construct five triangles under these conditions and 
draw the loci mentioned above. 

(C) VARIATION OF INDUCTANCE, THE RESISTANCE 

BEING CONSTANT. 

(a) Show what the locus of the current will be. 

(b) Give three different ways by which, without using 
iron, the inductance of the circuit may be varied. 

Get the data for, and construct five triangles as above, 
also construct the current locus. 

(D) BOTH INDUCTANCE AND RESISTANCE VARIED. 

(a) If both the inductance and the resistance vary 
proportionately what will be the effect on the angle of lag ? 

(b) How will the current vary? 

(E) VARIATION OF THE FREQUENCY. 

(a) Show what the locus of current will be when the 
frequency varies. 

(b) What will be the values of the current when the 
frequency is zero and when it is very large ? 


DYNAMO LABORATORY 


35 


Obtain triangles for five values of frequency, and con¬ 
struct the above locus. 

(F) INDUCTIVE CIRCUITS WITH IRON. 

(a) Why not use a solid iron core? 

(b) Explain the effect on the self-inductance of using 
different currents. 

(c) What will be the general nature of the curve of 
self-inductance with current? 

(d) How could the magnetic density of the iron be 
varied without changing the alternating current? 

N. L. M., Vol. ii, no. 

With five values of the alternating current construct 
the curve mentioned. Also try the effect of using a solid 
core. 

F. & W., Chs. I & V; N. L. M., Vol. II, 109 to 123; B. T., 63 to 70. 

30 . 

INDUCTIVE CIRCUITS IN SERIES AND PAR¬ 
ALLEL. 

(a) Show how to construct the E. M. F. diagram for 
several inductive circuits in series. 

(b) Also in parallel. 

Obtain the E. M. F. triangles for the different circuits 
given, and from them construct the diagrams for these 
circuits both in series and in parallel. Check these dia¬ 
grams by measurements on the circuits combined. 

B. T., 82 to 84; F. & W., Chap. VII. 

31 . 

CIRCUITS CONTAINING CAPACITY. 

(a) Upon what three things does the capacity of a 
condenser depend? 

(b) What two sources of loss in a condenser? 

(c) How do these losses show themselves in the 
action of a condenser? 


36 


NOTES AND QUESTIONS 


(B) IMPEDANCE DIAGRAM. 

(a) Explain the action of a condenser in producing 
a leading current in a circuit. 

(b) With an alternating current of given frequency, 
how obtain the capacity of a condenser ? 

(c) Discuss the effect of wave form on the result so 
obtained. 

(d) Show how to construct the E. M. F. and impe¬ 
dance diagrams for a circuit containing resistance, induct¬ 
ance and capacity. 

For the circuits given determine the E. M. F. and 
impedance diagrams. 


(C) VARIATION OF CAPACITY AND RESISTANCE. 

(a) Discuss and study these points as in the case of 
circuits with varying resistance and inductance. 


B. T., 70 to 77; F. & W., Chs. I & V; 
227 to 231, Vol. II, 170 to 178. 


N. L. M., Vol. I, 130 to 133, 


32 

CIRCUITS WITH CAPACITY IN SERIES AND IN 
PARALLEL. 

(a) Construct a diagram for the following six cir¬ 
cuits in series: (i) with R and L, (2) with R only, (3) with 
C only, (4) with R and C, (5) with R, L and C, (6) with L 
only. 

(b) For the same circuits in parallel. 

(c) What must be the value of the capacity to neu¬ 
tralize the inductance in a series circuit? 

(d) Show how to* determine graphically the value of 
the capacity in parallel necessary to bring a given lagging 
current into phase with its E. M. F. 

With the circuits and condensers given, construct and 
check by measurement series and parellel circuit diagrams; 
also calculate inductance and capacity to neutralize each 
other, and check by measurement. 

N. L. M., Vol. I, 227 to 231, Vol. II, 178, 


DYNAMO LABORATORY 


37 


33 . 

CURVE OF MAGNETIC DISTRIBUTION IN 
GENERATOR. 

(a) Describe a method for getting above curve for a 
generator when not running, using a ballistic galvano¬ 
meter. Why ballistic ? 

(b) In this case, just what do the ordinates of the 
curve represent? 

(c) Explain how to obtain the E. M. F. curve from 
this curve. 

(d) Would this be the same as the curve of E. M. F. 
obtained by the instantaneous contact method at full load, 
and why? 

Obtain the curve for one complete cycle and construct 
therefrom the E. M. F. curve. 

N. L. M., Vol. II, 107 to 109; Jackson, Vol. II, 266 to 271, 278 to 284, 
287 to 291. 

34 . 

CURVE OF EFFECTIVENESS OF ARMATURE 
TURNS IN PRODUCING REACTION ON 
THE FIELD. 

(a) What is the nature of the reaction produced by a 
coil when its center is under the middle of the pole-piece? 

(b) When the center is half way between the pole- 
pieces ? 

(c) Describe a method for obtaining a curve whose 
ordinates shall represent for each position under a pair oi 
poles, the effectiveness of the armature coils in producing 
forward and back reactions. 

(d) Show how, with this and the current curve to 
construct a curve proportional to the forward and back 
ampere-turns. 

(e) How v/ill this curve show whether the armature 
reactions will raise or lower the E. M. F. of the machine. 

Construct this effectiveness curve, and then with the 
current curve of the machine, or assuming a sine curve 



38 


NOTES AND QUESTIONS 


of current in phase with the E. M. F. construct the reaction 
curve; do the same for a current curve lagging 30°. 

35 . 

TRANSFORMERS, VOLTAGE RATIO AND 
REGULATION. 

(a) What is the relation of the primary and the 
secondary E. M. Fs. in a transformer? 

(b) At what load does the above relation hold ? 

(c) What approximate relation between the primary 
and secondary currents? 

(d) What prevents this relation from being exact? 

(e) With the same current densities in the primary 
and secondary, what is the relation of their resistances? 

(f) What are the sources of bad regulation in a 
transformer? 

(g) Give the formula for the most important of these 
causes of drop in voltage. 

(h) Give the steps to be taken to determine the reg¬ 
ulation, having but a single transformer to test? 

(i) How proceed if two similar transformers are 
available ? 

(j) Why is this method more accurate than the use 
of but one transformer? 

(k) What is the effect on the drop of varying the 
number of turns? 

( l ) What generally limits the drop that can be allowed 
in a transformer? 

(m) What is the effect of an inductive load on reg¬ 
ulation? Explain by use of diagram. 

(n) Define magnetic leakage. 

(o) How does magnetic leakage act in producing 
drop? Explain by use of diagram. 

(p) How is it best to arrange the windings of a 
transformer in order to reduce the leakage, and how effect¬ 
ive is this method ? 


DYNAMO LABORATORY 


39 


(q) A transformer suited to what special use can be 
made by constructing so as to exaggerate the leakage 
effect ? 

By varying the number of turns in the coils, prove the 
statement made in answers to (a) and (c). Measure resist* 
ances and note the agreement with (e). Calculate the 
copper drop for full load, measure the drop with a single 
transformer, and if two are available also by method of (i). 
Note the part of the drop due to leakage. 

Place inductances in the load and determine the curve 
of power-factor and drop with constant secondary current. 
By taking different combinations of coils in a one-to-one 
transformer, note effect of change in magnetic leakage on 
the drop. With transformer arranged to give large mag¬ 
netic leakage determine the current and E. M. F. charac¬ 
teristic for (q). 

F. & W., Ch. X; B. T., Ch. VII; Jackson, Vol. 426 to 450; T. D. E. M., 
694 to 700. 

36 . 

TRANSFORMERS, LOSSES AND EFFICIENCIES. 

(a) What are the sources of loss in a transformer? 

(b) Which are independent of the load? 

(c) How determine the iron losses? 

(d) Give methods of obtaining the copper losses. 

(e) What is the effect on the copper losses of in¬ 
creasing the number of turns? 

(f) What on the iron losses ? 

(g) In the ordinary transformer what would usually 
be the effect on the “all day efficiency” of increasing the 
number of turns, and why is this not done ? 

(h) Why is it better to measure the losses than the 
output and input in determining efficiencies? 

(i) What are the effects on the different losses, and 
on the losses as a whole, of increasing the periodicity? 

(j) The same for varying voltage? 

Measure the losses in the given transformer, and cal¬ 
culate the efficiencies for five loads. Plot the curve, 


40 


NOTES AND QUESTIONS 


Determine the iron losses for varying number of turns, 
for varying E. M. F. and for varying frequency, and plot 
curves. 

t „ F - & W. v 137 to 143; B. T. Ch. XVIII; Jackson, Vol. II, Ch. XI; N. 
L. M., Vol. II, 136 to 140. 


37 . 

STUDY OF POLYPHASE CURRENTS. 

(a) In a 2-phase 3-wire system, what relation does 
the current in the common return bear to that in the other 
wires ? 

(b) What is the relation of the E. M. Fs. in the above 
system ? 

(c) In a ring winding supplied by a 2-phase 4-wire 
system at points 90° apart what are the relations of the E. 
M. Fs. and currents in the quadrants and lines; demonstrate 
by diagrams ? 

(d) In this case why not use a system with a common 
return ? How can such be used with the addition of a one- 
to-one transformer? 

(e) Discuss L. M. Fs. and currents in a three-phase 
system, both star and mesh connected. 

Demonstrate the answers to the above experimentally. 

F. & W., Ch. VIII; Jackson, Vol. II, 546 to 555. 


38 . 

POLYPHASE POWER MEASUREMENT. 

(a) Give diagram showing connections of a watt¬ 
meter for measurement of power in 2-phase 4-wire, 2-phase 
3-wire, and 3-phase systems. 

(b) In a 2-phase 3-wire system, explain why, if the 
phases are exactly 90° apart, one wattmeter in the common 
return can be used, also the effect on these measurements 
if the phases are not exactly in quadrature. 

(c) Draw diagram for using one wattmeter and 
throw-over switches for a 2-phase 3-wire system. 


DYNAMO LABORATORY 


41 


(d) Explain how to use wattmeter to show if phases 
are exactly in quadrature. 

Connect up and measure the power in the circuits 
given. 

F. & W., 93; Jackson, Vol. II, 557 to 570. 

39 . 

POLYPHASE MOTORS. 

(a) How as compared with D. C. motors is the ratio 
of starting to full load running torque? 

(b) Explain the effect on the starting torque and on 
the regulation, of varying the resistance of the secondary. 

(c) Effect of varying the E. M. F. on the starting 
torque and on the speed. 

(d) Effect of varying the frequency on the speed of 
the motor. What determines the no-load speed of the 
motor? 

(e) Explain the object of the starting ring on motors 
with revolving primary. 

(f) Object of starting transformer with revolving 
secondary. 

(g) Effect on iron losses of using the revolving pri¬ 
mary. 

Get the starting torque of the motor and its relation 
to running torque at full load. Compare this with the 
same for direct current motors. Vary the resistance in the 
secondary and note effect on the starting torque and on the 
regulation. Vary the E. M. F. and note the difference in 
the starting torque and in the load necessary to stall the 
motor; plot curves. If practicable, note difference of 
temperature after short no-load run, of the iron in the 
primary and in the secondary. 

F. & W., Ch. XIV; Jackson, Vol. II, 591 to 633. 


42 


NOTES AND QUESTIONS 


40 . 

PARALLEL ALTERNATORS AND SYNCHRO¬ 
NOUS MOTORS. 

(a) What are the conditions which permit of elec¬ 
trically connecting two alternators, and how are those 
shown by the use of synchronizing lamps? 

(b) When an alternator is running as a motor, what 
is the effect of changing its excitation on the phase relation 
of the E. M. F. and current? Explain. 

(c) Explain the effect of changing the motor-load 
on the above phase relation ? 

(d) What is the effect of over-loading a synchronous 
motor ? 

(e) Explain how the counter E. M. F. is decreased 
with increase of load ? 

(f) Give three methods for telling whether a syn¬ 
chronous alternator is running as a motor or a generator. 

Run the machine as a synchronous motor and vary 
the field strength; with constant load determine curves of 
load current and phase angle with varying field current. 
Put an inductive circuit in parallel with the motor, and note 
the capacity effect of the motor. Running the machine as 
a motor, load it till it breaks • from synchronism. Plot 
curve between exciting current and load necessarv to pull 
out of step. Run two machines in parallel, and as the 
excitation of one is decreased note the change from gen¬ 
erator to motor. 

F. & W., Ch. XII. N. L. M., Vol. II, 144; Jackson, Vol. II, 571 to 590. 

41 . 

INSTANTANEOUS CONTACT METHOD AND 
GENERATOR CURVES. 

(a) Name two classes of contact makers (as to 
method of making the contact). 

(b) Describe three general methods of voltage deter¬ 
mination in instantaneous work. 


DYNAMO LABORATORY 


43 


(c) What is the usual method for obtaining the curves 
for current. 

(d) Give and explain the uses of condensers in instan¬ 
taneous contact work. 

(e) Draw diagram of circuits necessary to obtain E. 
M. F. and current curves from a generator. Show what 
part should be grounded and give effects on the readings 
of additional grounds at other parts of the circuits. 

(f) What is the effect of inductive and capacity loads 
on the regulation of a generator. Explain. 

Obtain E. M. F. and current curves for a generator 
by one or more methods, for no load, one-half load and 
full load, also for inductive load and capacity load. Note 
effect of latter on regulation. 

F. & w., Ch. II; N. L. M., Vol. II, 93 to 104; Jackson, Vol. II, 291 
to 304. 

42 . 

INSTANTANEOUS CURRENT AND E. M. F. 
CURVES ON TRANSFORMERS. 

(a) Draw diagram of circuits for determining trans¬ 
former curves. 

(b) Explain effect on curves of variation of load, of 
inductive load, of capacity load, and of too high density. 

(c) Show how, from the curves, to obtain watts sup¬ 
plied to the primary. 

Obtain complete curves for no load, one-half load and 
full load, also for inductive load and capacity load. Also 
by increase of voltage or decrease of number of turns, 
determine effect of too high density on the no-load current 
curve. 

B. T., Ch. XVII; Jackson, Vol. II, 450 to 460. 


APPENDIX. 


LABORATORY METHODS AND APPARATUS. 

No attempt will be made to give a complete discussion 
of these, but a few points that have proved especially success¬ 
ful will be mentioned. 

CALIBRATION ROOM. 

In order to encourage regular calibration of the instru¬ 
ments used, it is well to have a room fitted up so as to make 
this operation as convenient as possible; that is, so that it 
will only be necessary to connect in the instrument to be cali¬ 
brated, throw switches and adjust resistances. With such 
arrangements a calibration of all instruments once for every 
test is easily practicable. A convenient plan is to use a two 
or three scale standard voltmeter, having a low scale, say 
li volts, and with standard resistance, all calibrations both 
of current and voltage are referred to the same instrument. 

LABORATORY NOTE BOOKS. 

The student should learn to regard his note-book with 
the same esteem that an engineer does; it should be a re¬ 
pository of the original data and computed results, and not 
a copy-book to be valued chiefly for its nice appearance. 
For this purpose a standard note-book is desirable, one that 
shall be durable, convenient to carry in the pocket; not easily 
soiled, and of sufficient cost to make the student value it 
from the start. A form that has proven its usefulness may 
be described as follows: it has leather covers about 3! in. X 
6 \ in. with pages of good heavy paper; is is specially ruled, 
having besides a blue cross ruling about .16 in. apart red 
lines for every fifth each way and purple head-lines, making 



APPENDIX 


45 


it convenient for columns of figures, and also for simple 
curves, sketches, etc. Such a book may be made for 25 
cents each. 

CONNECTORS. 

A liberal supply of connectors is very important and 
very difficult to keep up. The difficulty has been solved by 
the laboratory having its own patterns and jigs and making 
a well designed connector with extra large wire holes and 
screws that completely fill these when screwed down. These 
are numbered in sets of four and are kept in a wall-case 
having a pigeon-hole for each number. The connectors 
are given out to the students at the beginning of the year 
on payment of a deposit and are seldom lost. 


XKtH3«l*A 






■ 

tetso-Ilsw £ ni Jrp>f 

















PART II. 





TABLES 

FOR 

ELECTRICAL ENGINEERS 


COMPILED BY 

F. C. CALDWELL 

H AND 

F. A. FISH 


COLUMBUS, OHIO 











j, 

Qd- n, Ijto 

£ tjdxArf 0X^3- d, 

* * ^ ^ 10 (y£> 


od>n, ,c f 


Copyright by 
F. C. Caldwell 
1900 


PRINTED AND FOR SALE BY 
FRED. J. HEER 
COLUMBUS, OHIO 


PREFACE. 


Among the following tables have been included only 
such as are of most frequent use to the electrical engineer. 
The aim has been to make these accurate to one-half per 
cent., after granting the assumptions upon which they are 
based, and which are in each case given. These features 
are unusual in wire tables. Tables similar to those for 
copper, have also been added for aluminum and iron. The 
latter represent average iron, but may be corrected for any 
other iron the exact specific resistance of which is known. 
The table for weight and thicknesses of insulations have been 
compiled as the average of a number of makes and will be 
useful as approximations. A number of other tables that 
are not usually found have been added. 



6 


TABLES FOR ELECTRICAL ENGINEERS 


PROPERTIES OF BARE COPPER AND ALUMINUM WIRE. 

£ Diam. Area Diam. Area pou n^pSlOWfeet ^ lo_ 

^ Mile Circular Milli- Cir 9“l ar Copper Alum- Alum- 

* MilS meters meter's sP Sr.-8.93 sp '”"3 67 C ° Ppe inum 

4° 460. 211600. 11.68 136.60 643.4 192.4 957. 286. 

3° 409.6 167800. 10.40 108.20 510.2 152.6 759. 227. 

2° 364.8 133100. 9.266 85.85 404.6 121.0 602. 180. 

0 324.9 105500. 8.251 68.08 320.9 95.92 478. 142.8 

1 

289.3 

83690. 

7.348 

53.99 

254.5 

76.08 

379. 

113.2 

2 

257.6 

66370. 

6.544 

42.82 

201.8 

60.34 

300. 

89.8 

3 

229.4 

52630. 

5.827 

33.96 

160.0 

47.85 

238. 

71.2 

4 

204.3 

41740. 

5.190 

26.93 

126.9 

37.95 

189. 

56.5 

5 

181.9 

33100. 

4.621 

21.35 

100.6 

30.09 

150. 

44.8 

6 

162.0 

26250. 

4.115 

16.94 

79.8 

23.86 

118.8 

35.5 

7 

144.3 

20820. 

3.665 

13.43 

63.3 

18.93 

94.2 

28.2 

8 

128.5 

16510. 

3.264 

10.65 

50.2 

15.01 

74.7 

22.34 

9 

114.4 

13090. 

2.906 

8.446 

39.8 

11.90 

59.2 

17.71 

10 

101.9 

10380. 

2.588 

6.699 

31.6 

9.44 

47.0 

14.05 

11 

90.74 

8234. 

2.305 

5.312 

25.04 

7.48 

37.3 

11.14 

12 

80.81 

6530. 

2.053 

4.213 

19.85 

5.94 

29.55 

8 83 

13 

71.96 

5178. 

1.828 

3.341 

15.74 

4.71 

23.43 

7.01 

14 

64.08 

4107. 

1.628 

2.649 

12.49 

3.73 

18.58 

5.56 

15 

57.07 

3257. 

1.450 

2.101 

9.90 

2.96 

14.74 

4.41 

16 

50.82 

2583. 

1.291 

1.666 

7.85 

2.348 

11.69 

3.49 

17 

45.26 

2048. 

1.150 

1.321 

6.23 

1.862 

9.27 

2.77 

18 

40.30 

1624. 

1.024 

1.048 

4.94 

1.477 

7.35 

2.355 

19 

35.89 

1288. 

.9116 

.8310 

3.92 

1.171 

5.83 

1.743 

20 

31.96 

1022. 

.8118 

.6590 

3.11 

.929 

4.62 

1.382 

21 

28.46 

810.1 

.7229 

.5226 

2.46 

.736 

3.67 

1.096 

22 

25.35 

642.5 

.6438 

.4145 

1.95 

.584 

2.907 

.869 

23 

22.57 

509.4 

.5733 

.3287 

1.55 

.463 

2.305 

.689 

24 

20.10 

404.0 

.5105 

.2607 

1.23 

.367 

1.828 

.547 . 

25 

17.90 

320.4 

.4546 

.2067 

.974 

.291 

1.450 

.433 

26 

15.94 

254.1 

.4049 

.1639 

.773 

.231 

1.150 

.344 

27 

14.20 

201.5 

.3605 

.1300 

.613 

.183 

.912 

.2726 

28 

12.64 

159.8 

.3211 

.1031 

.486 

.1453 

.723 

.2162 

29 

11.26 

126.7 

.2859 

.08177 

.385 

.1152 

.573 

.1714 

30 

10.025 

100.5 

.2546 

.06484 

.306 

.0914 

.455 

.1360 

31 

S.928 

79.71 

.2268 

.05142 

.242 

.0725 

.360 

.1078 

32 

7.950 

63.20 

.2019 

.04077 

.192 

.0575 

.286 

.0855 

33 

7.080 

50.13 

.1798 

.03234 

.1524 

.0456 

.227 

.0678 

34 

6.304 

39.74 

.1601 

.02564 

.1208 

.0361 

.180 

.0538 

35 

5.614 

31.52 

.1426 

.02034 

.0958 

.0287 

.1426 

.0426 

36 

5.000 

25.00 

.1270 

.01613 

.0760 

.0227 

.1131 

.0338 

37 

4.453 

19.83 

.1131 

.01279 

.0603 

.0180 

.0897 

.0268 

38 

3.965 

15.72 

.1007 

.01014 

.0478 

.0143 

.0711 

.0213 

39 

3.531 

12.47 

.08969 

.008044 

.0379 

.0113 

.0564 

.0169 

40 

3.144 

9.888 

.07986 

.006379 

.0301 

.0090 

.0447 

.0134 



















TABLES FOR ELECTRICAL ENGINEERS 


7 


RESISTANCE OF COPPER WIRE. 

*OHMS Differ- Differ- OHMS Differ- Differ- 

B.&S. No. per enee per ence per per kilo- enee per ence per 

1000 feet 10° F. 10° C. meter 10° F. 10° C. 

4° .04893 .00107 .00193 .1605 .00351 .0631 

3° .06170 .00132 .00243 .2024 .00443 .0797 

2° .07780 .00170 .00306 .2553 .00558 .1005 

0 .09811 .00214 .00386 .3219 .00704 .1267 

fFusing 

current 

1 

2 

3 

4 

5 

.1237 

.1560 

.1967 

.2480 

.3128 

.00270 

.00341 

.00430 

.00542 

.00684 

.00487 

.00614 

.00774 

.00976 

.0123 

.4059 

.5118 

.6454 

.8138 

1.026 

.00837 

.0112 

.0141 

.0178 

.0224 

.160 

.201 

.254 

.320 

.404 


6 

.3944 

.00862 

.0155 

1.294 

.0283 

.509 


7 

.4973 

.0109 

.0195 

1.632 

.0357 

.642 


8 

.6271 

.0137 

.0247 

2.058 

.0450 

.810 


9 

.7908 

.0173 

.0311 

2.595 

.0567 

1.021 


10 

.9972 

.0218 

.0392 

3.272 

.0715 

1.288 

333. 

11 

1.257 

.0275 

.0495 

4.126 

.0902 

1.62 

230. 

12 

1.586 

.0347 

.0624 

5.202 

.1138 

2.05 

235. 

13 

1.999 

.0437 

.0787 

6.545 

.1434 

2.58 

198. 

14 

2.521 

.0551 

.0992 

8.272 

.1809 

3.26 

166. 

15 

3.179 

.0695 

.1251 

10.67 

.2281 

4.10 

140. 

16 

4.009 

.OS77 

.1578 

13.15 

.288 

5.18 

117. 

17 

5.055 

.1105 

.199 

16 59 

.363 

6.53 

98.6 

IS 

6.374 

.1394 

.251 

20.91 

.457 

8.23 

82.9 

19 

8.038 

.1757 

.316 

26.37 

.577 

10.38 

69.7 

20 

10.14 

.2216 

.399 

33.25 

.727 

13.09 

58.5 

21 

12.78 

.2794 

.503 

41.93 

.917 

16.50 

49.2 

22 

16.12 

.3524 

.634 

52.87 

1.156 

20.81 

41.3 

23 

20.32 

.4443 

.800 

66.67 

1.458 

26.24 

34.7 

24 

25.63 

.5603 

1.009 

84.08 

1.838 

33.09 

29.2 

25 

32.31 

.7065 

1.272 

106.0 

2.265 

41.72 

24.5 

26 

40.75 

.891 

1.64 

133.7 

2.92 

52.61 

20.6 

27 

51.38 

1.123 

2.02 

168.6 

3.69 

66.34 

17.3 

28 

64.79 

1.417 

2.55 

212.6 

4.65 

83.66 

34.56 

29 

81.70 

1.786 

3.22 

268 0 

5.86 

105.5 

12.24 

30 

103 0 

2.252 

4.04 

338.0 

7.39 

133.0 

10.28 

31 

129.9 

2.84 

5.11 

426.2 

9.32 

167.7 

8.64 

32 

163.8 

3.58 

6.45 

537.4 

11.75 

211.5 

7.26 

33 

206.6 

4.55 

8.13 

677.7 

14.82 

266.7 

6.10 

34 

260.5 

5.70 

10.25 

854.6 

18.68 

336.3 

5.13 

35 

32S.4 

7.18 

12.93 

1078. 

23.56 

418.3 

4.31 

36 

414.2 

9.06 

16.30 

1359. 

29.7 

534.8 

3.62 

37 

522.2 

11.42 

20.55 

1713. 

37.5 

674.3 


38' 

658.5 

14.40 

25.92 

2161. 

47.2 

850.3 


39 

S30.4 

18.16 

32.68 

2718. 

59.6 

1072.0 


40 

1047.0 

22.9 

41.2 

3435. 

75.1 

1352.0 


♦At 68° F., or 20° C. Resistance of one circ. mil-foot is taken as 9.59 at 

0° C. 

fC = acP'; a for copper = 10244. 



































8 


TABLES FOR ELECTRICAL ENGINEERS 


No. B.&S. 

4° 

3° 

2° 

0 

RESISTANCE OF 

’•‘OHMS Differ- Differ- 

per enceper enceper 

1000 feet 10° F. 10° C. 

.08143 .00170 .00306 

.1027 .00214 .00384 

.1295 .00270 .00486 

.1633 .00341 .00613 

ALUMINUM WIRE. 

OHMS Differ- Differ- 

per kilo- enceper enceper 
meter 10° F. 10° C. 

.2672 .00557 .0100 

.3369 .00703 .0127 

.4248 .00886 .0160 

.5356 .0111 .0201 

fFusing 

current 

1 

.2059 

.00430 

.00773 

.6754 

.0141 

.0254 


2 

.2596 

.00542 

.00975 

.8517 

.0177 

.0320 


3 

.3274 

.00683 

.0123 

1.074 

.0224 

.0403 


4 

.4128 

.00861 

.0155 

1.354 

.0282 

.0509 


5 

.5205 

.0109 

.0196 

1.708 

.0356 

.0642 


6 

.6564 

.0137 

.0247 

2.163 

.0449 

.0809 


7 

.8277 

.0173 

.0311 

2.715 

.0567 

.102 


8 

1.044 

.0218 

.0392 

3.424 

.0715 

.129 


9 

1.316 

.0275 

.0494 

4.318 

.0901 

.162 


10 

1.659 

.0346 

.0623 

5.444 

.114 

.200 

247. 

11 

2.093 

.0437 

.0786 

6.865 

.143 

.258 

207. 

12 

2.639 

.0551 

.0991 

8.657 

.181 

.325 

174. 

13 

3.327 

.0694 

.125 

10.91 

.223 

.410 

146. 

14 

4.196 

.0876 

.158 

13.76 

.287 

.517 

123. 

15 

5.291 

.110 

.199 

17.76 

.362 

.652 

103. 

16 

6.671 

.139 

.251 

21.89 

.457 

.822 

86.9 

17 

8.412 

.176 

.316 

27.60 

.576 

1.04 

730 

18 

10.61 

.221 

.398 

34.80 

.726 

1.31 

61.4 

19 

13.38 

.279 

.502 

43.89 

916 

1.65 

51.6 

20 

16.87 

.352 

.634 

55.34 

1.15 

2.08 

43.3 

21 

21.27 

.444 

.799 

69.78 

1.46 

2.62 

36.4 

22 

26.82 

.560 

1.01 

87.99 

1.84 

3.31 

30.6 

23 

33.82 

.706 

1.27 

110.9 

2 32 

4.17 

25.7 

24 

42.64 

.890 

1.60 

139.9 

2.92 

5.26 

21.6 

25 

57.77 

1.12 

2.02 

176.4 

3.68 

6.63 

18.2 

26 

67.81 

1.42 

2.55 

222.5 

4.64 

S.36 

15.3 

27 

85.50 

1.78 

3.21 

230.5 

5.85 

10.5 

12.8 

28 

107.8 

2.25 

4.05 

353.7 

7.38 

13.3 

10.8 

29 

136.0 

2.84 

6.11 

446.0 

9.31 

16.8 

9 06 

30 

171.4 

3.58 

6.44 

562.5 

11.7 

21.1 

7.61 

31 

216.2 

4.51 

8.12 

709.2 

14.8 

26.6 

6.40 

32 

272.6 

5.69 

10.2 

894.3 

18.7 

33.6 

5.38 

33 

343.7 

7.17 

12.9 

1128.0 

23.5 

42.4 

4 52 

34 

423.6 

9.05 

16.3 

1422.0 

29.7 

53.4 

3. SO 

35 

546.6 

10.4 

20.1 

1793.0 

37.4 

67.4 

3.19 

36 

689.2 

14.4 

25.9 

2261.0 

47.2 

85.0 

2.63 

37 

869.1 

18.1 

32.6 

2851.0 

59.5 

107.0 

38 

1096.0 

22.9 

41.2 

3595.0 

75.0 

135.0 

- 

39 

1382.0 

28.8 

51.9 

4534.0 

94.6 

170.0 


40 

1743.0 

36.4 

65.5 

6717.0 

119. 

215.0 


♦At 
at 0° C. 

tc = 

68° F., 

= ad^, a 

or 20° C. Resistance of one circ. mil-foot taken = 15.983 

for aluminum =: 75S5. 









































TABLES FOR ELECTRICAL ENGINEERS 


9 




PROPERTIES OF IRON WIRE. 




Size 

B.W.G. 

Diam. 

mils 

Area 

circ. 

mils 

Diam. 
m. m. 

Area 
circ. 
m. m. 

^Pounds 
per 1000 
feet 

K iir S ' Nearest 

KffJ- W 

meter. iNO ' 

Diam. 
nearest 
B.& S. 
No. 


0 

340 

115600. 

8.636 

74.58 

304.5 

463.2 

0 

324.9 


1 

300 

90000. 

7.620 

58.06 

237.0 

352.7 

1 

289.3 


2 

284 

80656. 

7.214 

52.04 

212.5 

316.2 

1 

289.3 


3 

259 

67081. 

6.579 

43.28 

176.7 

263.0 

2 

257.6 


4 

238 

56644. 

6.045 

36.54 

149.2 

222.1 

3 

229.4 


5 

220 

48400. 

5.588 

31.23 

127.5 

189.8 

3 

229.4 


6 

203 

41209. 

5.156 

26.59 

108.6 

161.6 

4 

204.3 


7 

130 

32400. 

4.572 

20.90 

85.3 

127.0 

5 

181.9 


8 

165 

27225. 

4.191 

17.56 

71.7 

106.7 

6 

162.0 


9 

148 

21904. 

3.759 

14.13 

67.7 

85.9 

7 

144.3 


10 

134 

17956. 

3.404 

11.58 

47.3 

70.4 

8 

128.5 


11 

120 

14400. 

3.048 

9.290 

37.9 

56.5 

9 

114.4 


12 

109 

11881. 

2.769 

7.665 

31.3 

46.6 

9 

114.4 


13 

95 

9025. 

2.413 

5.822 

23.8 

35.4 

11 

90.74 


14 

83 

6889. 

2.108 

4.445 

18.1 

26.9 

12 

80.81 


15 

72 

5184. 

1.829 

3.344 

13.7 

20.3 

13 

71.96 


16 

65 

4225. 

1.651 

2.726 

11.13 

16.56 

14 

64.08 


17 

58 

3864. 

1.473 

2.170 

8.86 

13.19 

15 

57.07 


18 

49 

2401. 

1.245 

1.549 

6.33 

9.41 

16 

50.82 


19 

42 

1764. 

1.067 

1.138 

4.65 

6.92 

18 

40.30 


20 

35 

1225. 

.8890 

.7903 

3.23 

4.80 

19 

35.89 


21 

32 

1024. 

.8128 

.6606 

2.70 

4.015 

20 

31.96 


22 

28 

784. 

.7112 

.5058 

2.07 

3.074 

21 

28.46 


23 

25 

625. 

.6350 

.4032 

1.65 

2.450 

22 

25.35 


24 

22 

484. 

.5588 

.3123 

1.275 

1.897 

23 

22.57 


25 

20 

400. 

.5080 

.2581 

1.054 

1.568 

24 

20.10 


26 

18 

324. 

.4572 

.2090 

.854 

1.270 

25 

17.90 


27 

16 

256. 

.4064 

.1652 

.674 

1.004 

26 

15.94 


28 

14 

196. 

.3556 

.1265 

.516 

.768 

27 

14.20 


29 

13 

169. 

.3302 

.1090 

.445 

.663 

28 

12.64 


30 

12 

144. 

.3048 

.0929 

.379 

.565 

28 

12.64 


31 

10 

IDO. 

.2540 

.06452 

.2634 

.3920 

30 

10.025 


32 

9 

81. 

.2286 

.05226 

.2134 

.3176 

31 

8.928 


33 

8 

64. 

.2032 

.04129 

.1686 

.2509 

32 

7.950 


34 

7 

49. 

.1778 

.03161 

.1291 

.1921 

33 

7.080 


35 

5 

25. 

.1270 

.01613 

.0659 

.0980 

36 

5.000 


36 

4 

16. 

.1016 

.01032 

.0422 

.0627 

38 

3.965 


*583 pounds per cubic foot 

; weight per 1,000 feet = .002634xd*. 














10 


TABLES FOR ELECTRICAL ENGINEERS 


RESISTANCE OF IRON WIRE. 



-Ohms 

Differ- 

Differ- 

Ohms 

Differ- 

Differ- 

Feet per 

In O. 

Vt WT n 

per 1000 

ence per 

ence per 

per kilo- 

ence per 

ence per ohm at 


feet 

10° F. 

10° C. 

meter 

10° F. 

10 a C. 

180° F. 

0 

.649 

.0193 

.0348 

2.13 

.0634 

.114 

1078. 

l 

.834 

.0248 

.0447 

2.74 

.0814 

.147 

840. 

2 

.930 

.0277 

.0498 

3.05 

.0908 

.164 

752. 

3 

1.12 

.0333 

.0599 

3.67 

.109 

.197 

626. 

4 

1.32 

.0394 

.0710 

4.35 

.129 

.233 

528. 

5 

1.55 

.0461 

.0831 

5.09 

.151 

.273 

451. 

6 

1.82 

.0542 

.0976 

5.97 

.178 

.320 

384. 

7 

2.32 

.0689 

.124 

7.60 

.226 

.407 

302. 

8 

2.76 

.0820 

.148 

9.04 

.269 

.484 

254. 

9 

3.43 

.102 

.184 

11.2 

.334 

.602 

204. 

10 

4.18 

.124 

.224 

13.7 

.408 

.735 

167.5 

11 

5.21 

.155 

.279 

17.1 

.509 

.916 

134.3 

12 

6.32 

.188 

.338 

20.7 

.617 

1.11 

110.8 

13 

8.31 

.247 

.445 

27.3 

.812 

1.46 

84.2 

14 

10.9 

.324 

.584 

35.7 

1.06 

1.91 

64.3 

15 

14.5 

.431 

.775 

47.5 

1.41 

2.54 

48.4 

16 

17.8 

.529 

.952 

58.3 

1.73 

3.12 

39.4 

17 

22.3 

.664 

1.20 

73.2 

2.18 

3.92 

31.4 

18 

31.3 

.930 

1.67 

103. 

3.05 

5.49 

22.4 

19 

42.5 

1.27 

2.28 

140. 

4.15 

7.46 

16.45 

20 

61.3 

1.82 

3.28 

201. 

5.98 

10.8 

11 43 

21 

73.3 

2.18 

3.93 

240. 

7.16 

12.9 

9.55 

22 

95.7 

2.85 

5.13 

314. 

9.35 

16.8 

7.31 

23 

120. 

3.57 

6.43 

394. 

11.7 

21.1 

5.83 

24 

155. 

4.61 

8.31 

509. 

15.1 

27.3 

4.51 

25 

188. 

5.58 

10.1 

615. 

18.3 

33.0 

3.73 

26 

232. 

6.89 

12.4 

760. 

22.6 

40.7 

3.02 

27 

293. 

8.72 

15.7 

962. 

2S.6 

51.5 

2.39 

28 

383. 

11.4 

20.5 

1260. 

37.4 

67.3 

1.83 

29 

444. 

13.2 

23.8 

1460. 

43.3 

78.0 

1.58 

30 

521. 

15.5 

27.9 

1710. 

50.9 

91.6 

1.34 

31 

750. 

22.3 

40.2 

2460. 

73.3 

132.0 

.933 

32 

926. 

27.6 

49.6 

3040. 

90.5 

163 0 

.756 

33 

1170. 

84.9 

62.8 

3860. 

114.0 

206 0 

.570 

34 

1530. 

45.6 

82.0 

5020. 

150.0 

269.0 

.457 

35 

3000. 

89.3 

161.0 

9850. 

293.0 

528.0 

.233 

36 

4690. 

140.0 

251.0 

15400. 

458.0 

824.0 

.149 

•At 

68° F., 

o 

*1 

to 

o 

o 

O 

Resistance of one 

circ. mil-foot is 

taken as 67 


ohms at 0° C. 












TABLES FOR ELECTRICAL ENGINEERS 


11 


MAGNET WIRE. 


Single cotton covered. Double cotton covered. 


No. 

B. & S. 

Diam, 

mils 

Lbs. per 
1000 feet 

Feet per 
pound 

Turns 
per lin¬ 
ear in. 

Diam. 

Lbs. per 
1000 feet 

Feet per 
pound 

Turns 
per lin¬ 
ear inch 

1 





309 

259.3 

3.86 

3.2 

2 





278 

205.8 

4.87 

3.6 

3 





249 

163.4 

6.12 

4.0 

4 

216 

129 

7.75 

4.6 

224 

130.0 

7.70 

4.5 

5 

194 

102.5 

9.8 

5.1 

200 

102.9 

9.70 

5.0 

6 

172 

81.3 

12.3 

5.8 

180 

82.0 

12.2 

5.6 

7 

154 

64.4 

15.5 

6.5 

160 

65.0 

15.4 

6.2 

8 

138 

51.2 

19.5 

7.2 

144 

51.9 

19.3 

7.0 

9 

124. 

40.6 

24.6 

8.0 

130 

41.4 

24.1 

7.8 

10 

112 

32.3 

31.0 

8.9 

118 

33.0 

30.3 

8.5 

11 

101 

25.7 

38.9 

9.9 

107 

26.4 

37.9 

9.4 

12 

88 

20.3 

49.3 

11.3 

97 

21.1 

47.4 

10.3 

13 

79 

16.1 

62.1 

12.6 

88 

16.9 

59.2 

11.4 

14 

71 

12.8 

78.1 

14.1 

80 

13.5 

74.1 

12.5 

15 

64 

10.2 

98.0 

15.6 

71 

10.7 

93.5 

14.0 

16 

58 

8.1 

123.5 

17.2 

65 

8.6 

116.3 

15.4 

17 

50 

6.4 

156.2 

20.0 

57 

6.8 

147.1 

17.6 

18 

45 

5.1 

196.1 

22.2 

52 

5.4 

185.2 

19.3 

19 

41 

4.1 

244. 

24.4 

48 

4.37 

229.0 

20.8 

20 

37 

3.24 

309. 

27.0 

44 

3.54 

283.0 

22.7 

21 

33 

2.60 

3S5. 

30.3 

40 

2.86 

350. 

25.0 

22 

30 

2.07 

483. 

33.3 

37 

2.33 

430. 

27.0 

23 

27 

1.67 

600. 

37.0 

34 

1.91 

524. 

29.4 

24 

25 

1.33 

750. 

40.0 

32 

1.55 

645. 

31.2 

25 

23 

1.C6 

945. 

43.5 

30 

1.26 

794. 

33.3 

26 

21 

.85 

1175. 

47.5 

28 

1.03 

970. 

35.7 

27 

19 

.68 

1470. 

52.5 

26 

.83 

1200. 

38.5 

28 

18 

.54 

1850. 

55.5 

24 

.67 

1490. 

41.7 

29 

16 

.43 

2325. 

62.5 

23 

.55 

1820. 

43.5 

30 

15 

.34 

2940. 

66.6 

20 

.43 

2325. 

50.0 






















12 


TABLES FOR ELECTRICAL ENGINEERS 


TABLE OF MATERIALS. 



Tensile strength 
lbs. per sq. in. 

i 

•^Specific 

gravity. 

Wt. in lbs. per 

cu.in. 

Silver, annealed . 


10.5 

.379 

Copper, annealed . 

60000 

8.93 

.323 

Silver, hard . 




Copper, hard . 

32000 

8.89 

.321 

Gold, annealed . 


19.32 

.60S 

Gold, hard . 


Aluminum, av. com’l... 

24000 ) 

2.6) 

.091) 


to55000j 

-2.8 J 

-.102/ 

Aluminum, pure ann’l’d 


2.67 

.0964 

Zinc. 

7000 

6.86 

.248 

Brass (2 cop., 1 zinc).. 

45000 

8.55 

.309 

Platinum . 

53000 

20.3 

.733 

Iron, pure annealed. 


7.7 

.278 

Iron, av. com’l wire. 

56000 

7.75) 

.2,80) 



-7.85/ 

-.283/ 

Nickel . 


7 s 

282 

Tin . 

4600 

7.3 

.264 

Lead . 


11.45 

.414 

Ger. sil. (18% nickel).. 



Ger. sil. (30% nickel).. 




Platinoid . 




Plat. sil. (Pt. 67, Ag. 33) 




Antimony . 


6.7 

.242 

tMang. (Cu84,Ni4,Mnl2) 


Mercury . 


13 6 

491 

Bismuth . 


9.8 

.354 


Resistance at 

0° C. 

Temperature 

coefficient. 

Per circ. 

mil-foot 

Per circ. 

milli¬ 

meter 

From 0° 

to 20° C. 

From 0° 

to 100° C. 

9.02 

.0191 

'.00377 

.004 

9.59 

.0203 

.004 

.0042 

9.78 

.0207 



9.78 

.0207 



12.37 

.0262 

.00365 

.00377 

12.56 

.0266 



15.21 

.0322 / 



-17.8 ) 

-.0377 / 



15.98 

.0338 

.0039 

.0042 

33.75 

.0714 

.00365 

.004 

34.42 

.0728 



54.4 

.115 

.00376 

.00367 

57.5 

.122 

.005 

.0062 

67.0 

.142 

.006 

.006 

74.8 

.158 



79.3 

.168 



118.0 

.250 

.00387 

.0041 

1S7.9 

.398 

.00027 


292.3 

.619 

.00027 


201.4 

.426 

.00021 

.00031 

146.3 

.310 

.00031 

.00024 

213. 

.451 

.00389 


286. 

.605 

.00001 

.00001 

567.5 

1.20 

.00072 


787.3 

1.67 

.00354 



♦Water at 39.1° F., or 4° C. Weight of 1000 mil-feet of water at 4° 
C. = .0003405 pounds. 

t Manganin. 



























































TABLES FOR ELECTRICAL ENGINEERS 


13 


SPECIFIC RESISTANCE. 




Per mil-foot. 



Temp, in Cent. 

Temp, in Fahr. 

Copper. 

Aluminum. 

Average iron. 

0 

32 

9.59 

16.0 

67. 

5 

41 

9.78 

16.3 

69.0 

10 

50 

9.97 

16.6 

71.0 

15 

59 

10.14 

16.9 

73.0 

20 

68 

10.35 

17.3 

75.0 

25 

77 

10.55 

17.6 

77.0 

30 

86 

10.75 

17.9 

79.1 

35 

95 

10.95 

18.2 

81.1 

40 

104 

11.16 

18.5 

83.1 

45 

113 

11.36 

18.9 

85.1 

50 

122 

11.57 

19.2 

87.1 

55 

131 

11.77 

19.5 

89. \ 

60 

140 

11.98 

19.8 

91.1 

65 

149 

12.19 

20.1 

93.1 

70 

158 

12.40 

20.5 

95.2 

75 

167 

12.61 

20.8 

97.2 

80 

176 

12.82 

21.1 

99.2 

85 

185 

13.03 

21.4 

101.2 

90 

194 

13.23 

21.7 

103.2 

95 

203 

13.43 

22.1 

105.2 

100 

212 

13.64 

22.4 

107.2 


ENGLISH-METRIC. 

Equivalents. 


1 centimeter. 

1 inch. 

1 millimeter. 

1 mil. (.001 inch) 


.3937 inch. 
2.5400 cm. 
39.37 mils. 
.0254 mm. 


1 cir. mil. 
1 sq. mm. 
1 sq. mm. 
1 cir. mm. 


.000507 sq. mm. 
1973.5 cir mils. 
1.2732 qir. mm. 
.7854 sq. mm. 


1 meter. 

1 foot. 

1 kilometer. 
1 mile. 


3.2809 feet. 

.3048 m. 

.6214 mile. 
1.6093 kilometer. 


1 cir. mil. 

1 cir. mm. 

1 cubic cm. 

1 cubic inch. 


.0006452 cir. mm. 
1550 cir mils. 
.0610 cu. in. 
16.3867 cu. cms. 


1 sq. inch. 
1 sq. cm. 

1 sq. mil. 

1 cir mil. 


6.4516 sq 
.1550 sq. 
1.2732 cir. mil 
.7854 sq. mil. 


cms. 
in. 
mil. 


1 avoir, pound. 

1 kilogram. 

1 kilogr.—meter. 
1 foot-pound. 


.4536 kilogram 
2.2046 lbs. 

7.233 ft-lbs. 
.1383 lcilogr-m. 





























14 


TABLES FOR ELECTRICAL ENGINEERS 


CONVENTIONAL DIAGRAMS. 


DIRECT CURRENT 
MACHINE 



& 


AMMETER 


FUSE , 


JL 


GROUND' 



& 


ALTERNATOR. 


VOLTMETER 


-^VVWWW^— 


NON-INDUCTIVE 

RESISTANCE. 


-x-x-x-x- 

ARC CIRCUIT 



SERIES MACHINE 




WATTMETER 




INOUCTIVE 

RtSISTANCt. 




INCANDESCENT 

CIRCUIT 



¥ 


SHUNT MACHINE 


SWITCH 


TRANSFORMER 


INCANDESCENT 

LAMP 



COMPOUND MACHINE 


KNIFE SWITCH 


CR055IN6 WIRES 


CONDENSER 




BATTERY 


—WWWWW 


VARIABLE 

RESISTANCE 


JOINED WIRES 


PERIODS 


























































tables for electrical engineers 


15 


1,000 

1.0 


.9 

1.9 


1.7 


2,000 

1.6 

• • • • 

1.2 

2.1 


2.2 

2.4 

3,000 

1.8 

.... 

1.4 

2.4 


2.6 

3.8 

4,000 

2.0 

.... 

1.7 

2.8 


2.9 

6.4 

5,000 

2.2 

.... 

1.9 

3.2 

.... 

3.2 

10.8 

6,000 

2.4 


2.2 

3.6 


3.6 

17.4 

7,000 

2.8 

. . . . 

2.4 

4.1 

.... 

4.0 

26.8 

8,000 

3.1 

.... 

2.8 

4.8 

2.3 

4.6 

39.7 

9,000 

3.5 

.... 

3.4 

5.6 

2.9 

5.2 

58.0 

10,000 

3.8 

4.6 

4.0 

6.7 

3.5 

6.1 

.... 

11,000 

4.1 

5.0 

5.1 

8.0 

4.4 

7.2 


12,000 

4.8 

5.7 

6.6 

9.6 

5.6 

8.8 

.... 

13,000 

5.6 

7.0 

8.8 

11.6 

8.0 

11.2 

.... 

14,000 

7.3 

8.8 

12.7 

14.9 

12.4 

15.0 

.... 

15,000 

10.3 

13.2 

20.0 

*20.0 

20.6 

*22.0 

.... 

16,000 

16.4 

25.5 

27.4 

36.0 

36.0 

38.5 


17,000 

34.5 

44.5 

45.0 

72.0 

60.0 

80.0 

.... 

18,000 

72.0 

83.0 

78.0 

126.0 

100.0 

• • • . 

.... 

19,000 

120.0 

.... 

130.0 

.... 

165.0 

.... 

.... 


PERMEABILITY OF IRON. 

Magnetising force Magnetising force Magnetising force „ f 
\H) for Iron and (H) for Steel (H) for Armature 
Steel Forgings. Castings. Stampings. 


Cast Iron. 


The above values for wrought iron and steel are from curves published in 
the London Electrician, Vol. 39, page 670, and attributed to Ewing. Those for 
cast iron are given by Corsepius (1894). In the former minimum and maxi¬ 
mum values are given in each case. The curves from which the values are 
taken cross at the points marked *. 




































































Four Place 

Logarithmic and Trigonometric 
Tables 


ARRANGED BY 

F. C. CALDWELL 
1 \ 


Columbus, Ohio 








2 


MATHEMATICAL TABLES 


FOUR PLACE LOGARITHMS. 


Proportional parts. 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 2 

3 

4 

5 

6 

7 8 9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

4 8 12 

17 21 25 

29 33 37 

11 

0414 

0453 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

0765 

4 8 11 

15 19 23 

26 30 34 

12 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

1072 

1106 

3 7 10 

14 17 21 

24 28 31 

13 

1139 

1173 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

1430 

3 6 10 

13 16 19 

23 26 29 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

3 6 

9 

12 15 18 

21 24 27 

15 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

3 6 

8 

11 14 17 

20 22 25 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

3 5 

8 

11 13 16 

18 21 24 

17 

2304 

2330 

2355 

2380 

2406 

2430 

2455 

2480 

2504 

2529 

2 5 

7 

10 12 15 

17 20 22 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

2 5 

7 

9 12 14 

16 19 21 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

2 4 

7 

9 11 13 

16 18 20 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

2 4 

6 

8 11 13 

15 17 19 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

2 4 

6 

8 10 12 

14 16 18 

22 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

2 4 

6 

8 10 12 

14 15 17 

23 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

2 4 

6 

7 

9 11 

13 15 17 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

2 4 

5 

7 

9 11 

12 14 16 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

2 3 

5 

7 

9 10 

12 14 15 

26 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

2 3 

5 

7 

8 10 

11 13 15 

27 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

2 3 

5 

6 

8 

9 

11 13 14 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4664 

4579 

4594 

4609 

2 3 

5 

6 

8 

9 

11 12 14 

29 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757 

1 3 

4 

6 

7 

9 

10 12 13 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

1 3 

4 

6 

7 

9 

10 11 13 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

1 3 

4 

6 

7 

8 

10 11 12 

32 

5051 

5065 

5079 

5092 

5105 

5119 

5132 

5145 

5159 

5172 

1 3 

4 

5 

7 

8 

9 11 1? 

S3 

5185 

5198 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

1 3 

4 

5 

6 

8 

9 10 12 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

1 3 

4 

5 

6 

8 

9 10 11 

35 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

1 2 

4 

5 

6 

7 

9 10 11 

36 

5563 

5575 

6587 

5599 

5611 

5623 

5635 

5647 

5658 

6670 

1 2 

4 

5 

6 

7 

8 10 11 

37 

5682 

5694 

5705 

5717 

5729 

5740 

5752 

5763 

5775 

6786 

1 2 

3 

5 

6 

7 

8 9 10 

88 

5798 

5809 

5821 

5832 

5843 

5855 

6866 

5877 

58S8 

5899 

1 2 

3 

5 

6 

7 

8 9 10 

39 

5911 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

1 2 

3 

4 

5 

7 

8 9 10 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

1 2 

3 

4 

5 

6 

8 9 10 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

1 2 

3 

4 

5 

6 

7 8 9 

42 

6232 

6243 

6253 

6263 

6274 

62S4 

6294 

6304 

6314 

6325 

11 2 

3 

4 

5 

6 

7 8 9 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

1 2 

3 

4 

5 

6 

7 8 9 

44 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

6522 

1 2 

3 

4 

5 

6 

7 8 9 

45 

6532 

6542 

6551 

6561 

6571 

6580 

6590 

6599 

6609 

6618 

1 2 

3 

4 

5 

6 

7 8 9 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693 

6702 

6712 

1 2 

3 

4 

5 

6 

7 7 8 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785 

6794 

6803 

1 2 

3 

4 

5 

5 

6 7 8 

48 

6812 

6821 

6830 

6839 

6848 

6857 

6866 

6875 

6884 

6893 

1 2 

3 

4 

4 

5 

6 7 8 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

1 2 

3 

4 

4 

5 

6 7 8 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

1 2 

3 

3 

4 

5 

6 7 8 

51 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7135 

7143 

7152 

1 2 

3 

3 

4 

6 

6 7 8 

52 

7160 

7168 

7177 

7185 

7193 

7202 

7210 

7218 

7226 

7235 

1 2 

2 

3 

4 

5 

6 7 7 

53 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308 

7316 

!l 2 

2 

3 

4 

5 

6 6 7 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

1 2 

2 

3 

4 

5 

6 6 7 

55 

7404 

7412 

7419 

7427 

7435 

7443 

7451 

7459 

7466 

7474 

1 2 

2 

3 

4 

5 

5 6 7 

56 

7482 

7490 

7497 

7505 

7513 

7520 

7528 

7536 

7543 

7551 

1 2 

2 

3 

4 

5 

5 6 7 

57 

7559 

7566 

7574 

7682 

7589 

7697 

7604 

7612 

7619 

7627 

1 2 

2 

3 

4 

5 

5 6 7 

58 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694 

7701 

1 1 

2 

3 

4 

4 

5 6 7 

59 

7709 

7716 

7723 

7731 

7738 

7745 

7762 

7760 

7767 

7774 

1 1 

2 

3 

4 

4 

5 6 7 


0 

1 

2 

3 

4 | 

5 

6 

7 

8 

9 

1 2 

3 

4 

5 

6 

7 8 9 



































MATHEMATICAL TABLES 


3 


FOUR PLACE LOGARITHMS. 



0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

2 

3 

4 

5 6 

7 

8 

9 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

1 

1 

2 

3 

4 4 

5 

6 

6 

61 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910 

7917 

1 

1 

2 

3 

4 4 

5 

6 

6 

62 

7924 

7931 

7938 

7945 

7952 

7959 

7966 

7973 

7980 

7987 

1 

1 

2 

3 

3 4 

5 

6 

6 

63 

7993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048 

8055 

1 

1 

2 

3 

3 4 

5 

5 

6 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116 

8122 

1 

1 

2 

3 

3 4 

5 

5 

6 

65 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

1 

1 

2 

3 

3 4 

5 

5 

6 

66 

8195 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248 

8254 

1 

1 

2 

3 

3 4 

5 

5 

6 

67 

18261 

8267 

8274 

8280 

8287 

8293 

8299 

8306 

8312 

8319 1 

1 

1 

2 

3 

3 4 

5 

5 

6 

68 

8325 

8331 

8338 

8344 

8351 

8357 

8363 

8370 

8376 

8382 | 

1 

1 

2 

3 

3 4 

4 

5 

6 

69 

8388 

8395 

8401 

8407 

8414| 

8420 

8426 

8432 

8439 

8445 

1 

1 

2 

2 

3 4 

1 4 

5 

6 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

1 

1 

2 

2 

3 4 

4 

5 

6 

71 

8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555 

8561 

8567 

1 

1 

2 

2 

3 4 

4 

5 

5 

72 

8573 

8579 

8585 

8591 

8597 

8603 

8609 

8615 

8621 

8627 

1 

1 

2 

2 

3 4 

4 

5 

5 

73 

8633 

S639 

8645 

8651 

8657 

8663 

8669 

8675 

8681 

8686 

1 

1 

2 

2 

3 4 

4 

5 

5 

74 

8692 

8698 

8704 

8710 

8716 

8722 

8727 

8733 

8739 

8745 

1 

1 

2 

2 

3 4 

4 

5 

5 

75 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

1 

1 

2 

2 

3 3 

4 

5 

5 

76 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854 

8859 

1 

1 

2 

2 

3 3 

4 

5 

5 

77 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8904 

8910 

8915 

1 

1 

2 

2 

3 3 

4 

4 

5 

78 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965 

8971 

1 

1 

2 

2 

3 3 

4 

4 

5 

79 

|8976 

8982 

8987 

8993 

8998 

9004 

9009 

9015 

9020 

9025 

1 

1 

2 

2 

3 3 

4 

4 

5 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

1 

1 

2 

2 

3 3 

4 

4 

5 

81 

9085 

9090 

9096 

9101 

9106 

9112 

9117 

9122 

9128 

9133 

1 

1 

2 

2 

3 3 

4 

4 

5 

82 

9138 

9143 

9149 

9154 

9159 

9165 

9170 

9175 

9180 

9186 

1 

1 

2 

2 

3 3 

4 

4 

5 

83 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232 

9238 

1 

1 

2 

2 

3 3 

4 

4 

5 

84 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284 

9289 

1 

1 

2 

2 

3 3 

4 

4 

5 

85 

9294 

9299 

9304 

9309 

9315 

9320 

9325 

9330 

9335 

9340 

1 

1 

2 

2 

3 3 

4 

4 

5 

86 

9345 

9350 

9355 

9360 

9365 

9370 

9375 

9380 

9385 

9390 

1 

1 

2 

2 

3 3 

4 

4 

5 

87 

9395 

9400 

9405 

9410 

9415 

9420 

9425 

9430 

9435 

9440 

0 

1 

1 

2 

2 3 

3 

4 

4 

88 

9445 

9450 

9455 

9460 

9465 

9469 

9474 

9479 

9484 

9489 

0 

1 

1 

2 

2 3 

3 

4 

4 

89 

9494 

9499 

9504 

9509 

9513 

9518 

9523 

9528 

9533 

9538 

0 

1 

1 

2 

2 3 

3 

4 

4 

90 

9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581 

9586 

0 

1 

1 

2 

2 3 

3 

4 

4 

91 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628 

9633 

0 

1 

1 

2 

2 3 

3 

4 

4 

92 

9633 

9643 

9647 

9652 

9657 

9661 

9666 

9671 

9675 

9680 

0 

1 

1 

2 

2 3 

3 

4 

4 

93 

9685 

9689 

9694 

9699 

9703 

9708 

9713 

9717 

9722 

9727 

0 

1 

1 

2 

2 3 

3 

4 

4 

94 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

0 

1 

1 

2 

2 3 

3 

4 

4 

95 19777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

0 

1 

1 

2 

2 3 

3 

4 

4 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

0 

1 

1 

2 

2 3 

3 

4 

4 

97 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

9899 

9903 

9908 

0 

1 

1 

2 

2 3 

3 

4 

4 

98 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

0 

1 

1 

2 

2 3 

3 

4 

4 

99 

19956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

9996 

0 

1 

1 

2 

2 3 

3 

3 

4 

100 

0000 

0004 

0009 

0013 

0017 

0022 

0026 

0030 

0035 

0039 

0 

1 

1 

2 

2 3 

3 

3 

4 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

2 

3 

4 

5 6 

7 

8 

9 


Proportional parts. 


II. 22 /7 

Naperian base, e.... 

Modulus, M . 

g, feet per second... 
g, cm. per second.. 
Mech. equivalent— 
Gm. Cu. per amp hr. 

Watts in HP. 

Foot lbs in HP.... 


Number. 

Log. 


3.1416 

2.7183 

.4343 

oo 9 

10.49715 

0.4343 

1.6378 

1.5079 

2.9913 

2.8910 

0.0708 

2.8727 

4.5185 

TnrTie<; in meter. 

Cm in inch. 

Cm in foot.. 

Feet in meter.. 

980.2 

778 

1.177 

746 

33000 

Km in mile.. 

Sq. cm. in sq. inch. 

Cu cm. in cu. inch. 

dm in minre avoir. 

Lbs. in kilogram. 


Num¬ 

ber. 


39.3704 

2.5400 

30.480 

3.2808 

1.6093 

6.4516 

16,387 

28,350 

2.2046 


Log. 


1.5952 

0.4048 

1.4840 

0.5160 

0.2067 

0.8097 

1.2145 

0.4526 

0.3433 












































































4 


MATHEMATICAL TABLES 


TABLE OF SINES AND COSINES. 


Sine 

0 

Cos 

60' 

0' 

Sin 

50' 

10' 

40' 

20' 

oo 

CO CO 

20' 

40 7 

lO' 

50' 

Cos 

0' 

60' 

Sin 

Cos 

O 

Dif. 

0 

0000 

0029 

0058 

0087 

0116 

0146 

0174 

89 

29 

1 

0174 

0204 

0233 

0262 

0291 

0320 

0349 

88 

29 

2 

0349 

0378 

0407 

0436 

0465 

0494 

0523 

87 

29 

3 

0523 

0552 

0581 

0610 

0639 

0668 

0698 

86 

29 

4 

0698 

0727 

0756 

0785 

0814 

0843 

0872 

85 

29 

5 

0872 

0900 

0929 

0958 

0987 

1016 

1046 

84 

29 

6 

1045 

1074 

1103 

1132 

1161 

1190 

1219 

83 

29 

7 

1219 

1248 

1276 

1305 

1334 

1363 

1392 

82 

29 

8 

1392 

1420 

1449 

1478 

1507 

1536 

1564 

81 

29 

9 

1564 

1593 

1622 

1650 

1679 

1708 

1736 

80 

.29 

10 

1736 

1765 

1794 

1822 

1851 

1879 

1903 

79 

29 

11 

1908 

1937 

1965 

1994 

2022 

2051 

2079 

78 

29 

12 

2079 

2108 

2136 

2164 

2193 

2221 

2249 

77 

28 

13 

2249 

2278 

2306 

2334 

2363 

2391 

2419 

76 

28 

14 

2419 

2447 

2476 

2504 

2532 

2560 

2588 

76 

28 

15 

2588 

2616 

2644 

2672 

2700 

2728 

2756 

74 

28 

16 

2756 

2784 

2812 

2840 

2368 

2896 

2924 

73 

28 

17 

2924 

2951 

2979 

3007 

3035 

3062 

3090 

72 

28 

18 

3090 

3118 

3145 

3173 

3201 

3228 

3256 

71 

28 

19 

3256 

3283 

3310 

3338 

3365 

3393 

3420 

70 

27 

20 

3420 

3447 

3475 

3502 

3529 

3556 

3584 

69 

27 

21 

3584 

3611 

3638 

3665 

3692 

3719 

3746 

68 

27 

22 

3746 

3773 

3800 

3827 

3854 

3880 

3907 

67 

27 

23 

3907 

3934 

3961 

3937 

4014 

4041 

4067 

66 

27 

24 

4067 

4094 

4120 

4147 

4173 

4200 

4226 

65 

27 

25 

4226 

4252 

4279 

4305 

4331 

4357 

4384 

64 

26 

26 

4384 

4410 

4436 

4462 

4483 

4514 

4540 

63 

26 

27 

4540 

4566 

4592 

4617 

4643 

4669 

4695 

62 

26 

28 

4695 

4720 

4746 

4772 

4797 

4823 

4848 

61 

26 

29 

4848 

4873 

4899 

4924 

4949 

4975 

5000 

60 

25 

30 

5000 

5025 

5050 

5075 

5100 

5125 

5150 

59 

25 

31 

5150 

5175 

5200 

5225 

6250 

5274 

5299 

58 

25 

32 

5299 

5324 

5348 

5373 

5397 

5422 

6446 

57 

25 

33 

5446 

5471 

6495 

5519 

5544 

6568 

5592 

56 

24 

34 

5592 

5616 

5640 

5664 

5688 

5712 

5736 

55 

24 

35 

5736 

6760 

5733 

5807 

5831 

5854 

5878 

54 

24 

36 

5878 

5901 

5925 

6948 

5972 

5995 

6018 

53 

23 

37 

G018 

6041 

6064 

6088 

6111 

6134 

6157 

52 

23 

38 

6157 

6179 

6202 

6225 

6248 

6271 

6293 

51 

23 

39 

6293 

6316 

6338 

6361 

6383 

6406 

6428 

50 

23 

40 

6428 

6450 

6472 

6494 

6517 

6639 

6561 

49 

22 

41 

6561 

6582 

6604 

6626 

6648 

6670 

6691 

48 

22 

42 

6691 

6713 

6734 

6756 

6777 

6799 

6820 

47 

22 

43 

6320 

6841 

6862 

6883 

6905 

6926 

6947 

46 

21 

44 

6947 

6967 

69S8 

7009 

7030 

7050 

7071 

45 

21 

45 | 

| 7071 

7092 

7112 | 

7132 | 

7163 

7173 

7193 || 44 1 

! 20 


Cos 






Cos 



o 

60' 

50' 

40' 

30' 

20' 

lO' 

0' 

O 


Sine 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

Cos 

Dif. 


Sin 






Sin 



















































MATHEMATICAL TABLES 


5 


TABLE OF SINES AND COSINES. 


Sine 

O 

Cos. 

60' 

O' 

Sin. 

50' 

10' 

40' 

20' 

30' 

30' 

20' 

40' 

10' 

50' 

Cos. 

0' 

60' 

Sin. 

Cos. 

O 

Dif. 

45 

7071 

7092 

7112 

7132 

7153 

7173 

7193 

44 

20 

46 

7193 

7214 

7234 

7254 

7274 

7294 

7313 

43 

20 

47 

7313 

7333 

7353 

7373 

7392 

7412 

7431 

42 

20 

48 

7431 

7451 

7470 

7490 

7509 

7528 

7547 

41 

19 

4D 

7547 

7566 

7585 

7604 

7623 

7642 

7660 

40 

19 

50 

7660 

7679 

7698 

7716 

7735 

7753 

7771 

39 

18 

51 

7771 

7790 

7808 

7826 

7844 

7862 

78S0 

38 

18 

52 

7880 

7898 

7916 

7933 

7951 

7969 

7986 

37 

18 

53 

7986 

8004 

8021 

8039 

8056 

8073 

8090 

36 

17 

54 

8090 

8107 

8124 

8141 

8158 

8175 

8191 

35 

17 

55 

8191 

8208 

8225 

S241 

8258 

8274 

8290 

34 

17 

56 

8290 

8307 

8323 

8339 

8355 

8371 

8387 

33 

16 

57 

8387 

8402 

8418 

8434 

8449 

8465 

8480 

32 

16 

58 

8480 

8496 

8511 

8526 

8542 

8557 

8572 

31 

15 

59 

8572 

8587 

8601 

8616 

8631 

8646 

8660 

30 

15 

60 

8660 

8675 

8689 

8704 

8718 

8732 

8746 

29 

14 

61 

8746 

8760 

8774 

8788 

8802 

8816 

8829 

28 

14 

62 

8829 

8843 

8S57 

8870 

8883 

8897 

8910 

27 

13 

63 

8910 

8923 

8936 

8949 

8962 

8975 

8988 

26 

13 

64 

8988 

9001 

9013 

9026 

9038 

9051 

9063 

25 

12 

65 

9063 

9075 

9087 

9100 

9112 

9124 

9135 

24 

12 

66 

9135 

9147 

9159 

9171 

9182 

9194 

9205 

23 

12 

67 

9205 

9216 

9228 

9239 

9250 

9261 

9272 

22 

11 

68 

9272 

9283 

• 9293 

9304 

9315 

9325 

9336 

21 

11 

69 

9336 

9346 

9356 

9367 

9377 

9387 

9397 

20 

10 

70 

9397 

9407 

9417 

9426 

9436 

9446 

9455 

19 

10 

71 

9455 

9465 

9474 

9483 

9492 

9501 

9511 

18 

09 

72 

9511 

9519 

9528 

9537 

9546 

9554 

9563 

17 

09 

73 

9563 

9571 

9580 

9588 

9596 

9605 

9613 

16 

08 

74 

9613 

9621 

9628 

9636 

9644 

9652 

9659 

15 

| 08 

75 

9659 

9667 

9674 

9681 

9689 

9696 

9703 

14 

07 

76 

9703 

9710 

9717 

9724 

9730 

9737 

9744 

13 

07 

77 

9744 

9750 

9757 

9763 

9769 

9775 

9781 

12 

06 

78 

9781 

9787 

9793 

9799 

9805 

9811 

9816 

11 

06 

79 

9816 

9822 

9827 

9832 

9838 

9843 

9848 

10 

05 

SO 

9848 

9853 

9858 

9863 

9868 

9872 

9877 

9 

05 

81 

9877 

9881 

9886 

9890 

9894 

9899 

9903 

8 

04 

82 

9903 

9907 

9911 

9914 

9918 

9922 

9925 

7 

04 

S3 

9925 

9929 

9932 

9936 

9939 

9942 

9945 

6 

03 

84 

9945 

9948 

9951 

9954 

9957 

9959 

9962 

5 

03 

85 

9962 

9964 

9967 

9969 

9971 

9974 

9976 

4 

02 

86 

9976 

9978 

9979 

9981 

9983 

9985 

9986 

3 

02 

87 

99S6 

9988 

9989 

9990 

9992 

9993 

9994 

2 

01 

88 

9994 

9995 

9996 

9997 

9997 

9998 

9998 

1 

01 

89 

999S 

9999 

9999 

0000 

0000 

0000 

0000 

0 

00 


Cos. 






Co s. 



O 

60' 

50' 

40 

30' 

20' 

10' 

o' 

o 

Dif 

Sine 

O' 

10' 

20' 

30' 

40' 

50' 

60' 

Cos. 



Sin. 






Sin. 









































































































6 


MATHEMATICAL TABLES 


TABLE OF TANGENTS AND COTANGENTS. 


Tang. 

O 

Cot. 

60' 

O' 

Tan. 

50' 

10' 

40' 

20' 

30' 

30 7 

2 <y 

40' 

10' 

50' 

Cot. 

O' 

60 7 

Tan. 

Cot. 

O 

Dif. 

0 

0000 

0029 

0058 

0087 

0116 

0145 

0175 

89 

29-29 

1 

0175 

0204 

0233 

0262 

0291 

0320 

0349 

88 

29-29 

2 

0349 

0378 

0407 

0437 

0466 

0495 

0524 

87 

29-29 

3 

0524 

0553 

0582 

0612 

0641 

0670 

0699 

86 

29-29 

4 

0699 

0728 

0758 

0787 

0816 

0846 

0875 

85 

29-29 

5 

0875 

0904 

0933 

0963 

0992 

1022 

1051 

84 

29-29 

6 

1051 

1080 

1110 

1139 

1169 

1198 

1228 

83 

29-29 

7 

1228 

1257 

1287 

1316 

1346 

1376 

1405 

82 

29-29 

8 

1405 

1435 

1465 

1494 

1524 

1554 

1584 

81 

80-30 

9 

1534 

1614 

1643 

1673 

1703 

1733 

1763 

80 

30-30 

10 

1763 

1793 

1823 

1853 

1883 

1914 

1944 

79 

30-30 

11 

1944 

1974 

2004 

2034 

2065 

2095 

2126 

78 

30-30 

12 

2126 

2156 

2186 

2217 

2247 

2278 

2309 

77 

30-30 

13 

2309 

2339 

2370 

2401 

2432 

2462 

2493 

76 

30-31 

14 

2493 

2524 

2555 

2586 

2617 

2648 

2679 

75 

31-31 

15 

2679 

2711 

2742 

2773 

2805 

2836 

2867 

74 

31-31 

16 

2867 

2899 

2930 

2962 

2994 

3025 

3057 

73 

32-32 

17 

3057 

3039 

3121 

3153 

3185 

3217 

3249 

72 

32-32 

18 

3249 

3281 

3314 

3346 

3378 

3411 

3443 

71 

32-32 

19 

3443 

3476 

3508 

3541 

3574 

3607 

3640 

70 

33-33 

20 

3640 

3673 

3706 

3739 

3772 

3805 

3839 

69 

33-34 

21 

3839 

3872 

3905 

3939 

3973 

4006 

4040 

68 

34-34 

22 

4040 

4074 

4108 

4142 

4176 

4210 

4245 

67 

34-35 

23 

4245 

4279 

4314 

4348 

4383 

4417 

.4452 

66 

35-35 

24 

4452 

4487 

4522 

4557 

4592 

4628 

4663 

65 

35-35 

25 

4663 

4698 

4734 

4770 

4805 

4841 

4877 

64 

35-36 

26 

4877 

4913 

4949 

4986 

5022 

5059 

5095 

63 

36-36 

27 

5095 

5132 

5169 

5206 

5243 

5280 

5317 

62 

37-37 

28 

5317 

5354 

5392 

5430 

5467 

5505 

5543 

61 

37-38 

29 

5543 

5581 

5619 

5658 

5696 

5735 

5773 

60 

38-38 

30 

5773 

5812 

5851 

5890 

5930 

5969 

6009 

59 

39-40 

31 

6009 

6048 

6088 

6128 

6168 

6208 

6249 

58 

40-41 

32 

6249 

62S9 

6330 

6371 

6412 

6453 

6494 

57 

41-41 

33 

6494 

6535 

6577 

6619 

6661 

6703 

6745 

56 

41-42 

34 

6745 

6737 

6830 

6873 

6916 

6959 

7002 

55 

42-43 

35 

7002 

7045 

7089 

7133 

7177 

7221 

7265 

54 

43-44 

36 

7265 

7310 

7355 

7400 

7445 

7490 

7535 

63 

45-45 

37 

7535 

7531 

7627 

7673 

7720 

7766 

7813 

52 

46-47 

38 

7813 

7860 

7907 

7954 

8002 

8050 

8098 

51 

47-48 

39 

809S 

8146 

8195 

8243 

8292 

8341 

8391 

50 

43-50 

40 

8391 

8441 

8491 

8541 

8591 

8642 

8693 

49 

50-51 

41 

8693 

8744 

8795 

8347 

8899 

8951 

9004 

48 

51-53 

42 

9004 

9057 

9110 

9163 

9217 

9271 

9325 

47 

53-54 

43 

9325 

9380 

9434 

9490 

9545 

9601 

9657 

46 

55 56 

44 

9657 

9713 

9770 

9S27 

9884 

9942 

1.0000 

45 

56-58 

45 

11.0000 

1.0053 

1.0117 

1.0176 

1.0235 

1.0295 

1.0355 | 

I 4* 

58-60 


Cot. 






Cot. 



o 

60' 

50' 

40' 

30' 

20' 

10' 

O' 

O 


Tang. 

0' 

10' 

20' 

SO 7 

10 7 

50' 

60' 

Cot. 

Dif. 


Tan. 






Tan. 


































































































MATHEMATICAL TABLES 


7 


TABLE OF TANGENTS AND COTANGENTS. 


Tan. 

O 

Cot. 

60' 

O' 

Tan. 

50' 

10' 

40' 

20' 

30' 

30' 


10' 

50' 

Cot. 

O' 

60' 

Tan. 

Cot 

o 

Dif. 

45 

1.000 

1.006 

1.012 

1.018 

1.024 

1.030 

1.036 

44 

.006-.006 

46 

1.036 

1.042 

1.048 

1.054 

1.060 

1.066 

1.072 

43 

.006-.006 

47 

1.072 

1.079 

1.085 

1.091 

1.098 

1.104 

1.111 

42 

.007-.007 

48 

1.111 

1.117 

1.124 

1.130 

1.137 

1.144 

1.150 

41 

.007-.007 

49 

1.150 

1.157 

1.164 

1.171 

1.178 

1.185 

1.192 

40 

.007-.007 

50 

1.192 

1.199 

1.206 

1.213 

1.220 

1.228 

1.235 

39 

.007-.007 

51 

1.235 

1.242 

1.250 

1.257 

1.265 

1.272 

1.280 

38 

.007-.008 

52 

1.280 

1.288 

1.295 

1.303 

1.311 

1.319 

1.327 

37 

.008-.008 

53 

1.327 

1.335 

1.343 

1.351 

1.360 

1.368 

1.376 

36 

.008-.008 

54 

1.376 

1.385 

1.393 

1.402 

1.411 

1.419 

1.428 

35 

.009-.009 

65 

1.428 

1.437 

1.446 

1.455 

1.464 

1.473 

1.483 

34 

.009-.010 

56 

1.4SS 

1.492 

1.501 

1.511 

1.520 

1.530 

1.540 

33 

.009-. 010 

57 

1.540 

1.550 

1.560 

1.570 

1.580 

1.590 

1.600 

32 

•010-.010 

58 

1.600 

1.611 

1.621 

1.632 

1.643 

1.653 

1.664 

31 

•011-.011 

59 

1.664 

1.675 

1.686 

1.698 

1.709 

1.720 

1.732 

30 

.011-.012 

60 

1.732 

1.744 

1.756 | 

1.767 

1.780 

1.792 

1.804 | 

1 29 

| .012-.012 

61 

1.804 

1.816 

1.829 

1.842 

1.855 

1.868 

1.881 

28 

.012-.013 

62 

1.881 

1.894 

1.907 

1.921 

1.935 

1.949 

1.963 

27 

.014-.014 

63 

1.963 

1.977 

1.991 

2.006 

2.020 

2.035 

2.050 

26 

.014-.015 

64 

2.050 

2.065 

2.081 

2.097 

2.112 

2.128 

2.145 

25 

.015-.016 

65 

2.145 

2.161 

2.177 

2.194 

2.211 

2.229 

2.246 

24 

.016-.017 

66 

2.246 

2.264 

2.282 

2.300 

2.318 

2.337 

2.356 

23 

.018-.019 

67 

2.356 

2.375 

2.394 

2.414 

2.434 

2.455 

2.475 

22 

.019-.021 

68 

2.475 

2.496 

2.517 

2.539 

2.560 

2.583 

2.605 

21 

.021-.022 

69 

2.605 

2.628 

2.651 

2.675 | 

| 2.699 

2.723 

2.747 

20 

.023-.024 

70 

2.747 

2.773 

2.798 

2.824 

2.850 

2.877 

2.904 

19 

.025-.027 

71 

2.904 

2.932 

2.960 

2.989 

3.018 

3.047 

3.078 

18 

.028-.031 

72 

3.078 

3.108 

3.140 

3.172 

3.204 

3.237 

3.271 

17 

.031-.034 

73 

3.271 

3.305 

3.340 

3.376 

3.412 

3.450 

3.487 

16 

.034-.038 

74 

3.487 

3.526 

3.566 

3.606 

3.647 

3.689 

3.732 

15 

.039-.043 

75 

3.732 

3.776 

3.821 

3.867 

3.914 

3.962 

4.011 

14 

.044-.049 

76 

4.011 

4.061 

4.113 

4.165 

4.219 

4.275 

4.332 

13 

.050-.057 

77 

4.332 

4.390 

4.449 

4.511 

4.574 

4.638 

4.705 

12 

.058-.067 

78 

4.705 

4.773 

4.843 

4.915 

4.989 

5.066 

5.145 

11 

.068-.079 

79 

5.145 

5.226 

5.809 

5.396 

5.484 

5.576 

5.671 

10 

.081-.095 

80 

5.671 

5.769 

5.871 

5.976 

6.084 

6.197 

6.314 

9 

.098-.107 

81 

6.314 

6.435 

6.561 

6.691 

6.827 

6.968 

7.115 

8 

.121-.147 

82 

7.115 

7.269 

7.429 

7.596 

7.770 

7.953 

8.144 

7 

.154-.191 

83 

8.144 

8.345 

8.556 

8.777 

9.010 

9.255 

9.514 

6 

.231-.259 

84 

9.514 

9.788 

10.08 

10.39 

10.71 

11.06 

11.43 

5 

.274-.37 

85 

11.43 

11.83 

12.25 

12.71 

13.20 

13.73 

14.30 

4 

.40 -.57 

86 

14.30 

14.92 

15.60 

16.35 

17.17 

18.07 

19.08 

3 

.62 -1.01 

87 

19.08 

20.21 

21.47 

22.90 

24.54 

26.43 

28.64 

2 

1.13 -2.21 

88 

28.64 

31.24 

34.37 

38.19 

42.96 

49.10 

57.29 

1 

2.60 -8.19 

89 

57.29 

68.75 

85.94 

114.6 

171.9 

343.8 

OO 

0 

11.46-oc 


Cot. 






Cot. 



0 

60' 

50' 

40' 

30' 

20' 

10' 

O' 

° 

nif 

Tan. 

O' 

10' 

20' 

30' 

40' 

50' 

60' 

Cot 

XJ 11 . 


Tan. 






Tan. 











































■ 

















































* 






1 



















